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Common Core: High School - Number and Quantity : Matrices Operations (Add, Subtract, and Multiply): CCSS.Math.Content.HSN-VM.C.8

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Example Questions

Example Question #213 : High School: Number And Quantity

Compute the sum of the two matrices.

$\begin{bmatrix} 4 & 10 & -3\\ 7& -11& 4 \end{bmatrix} + \begin{bmatrix} 2&-8 &3 \\ -6&11 & 2 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 4 & 10 & -3\\ 7& -11& 4 \end{bmatrix} + \begin{bmatrix} 2&-8 &3 \\ -6&11 & 2 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 2&18 &0 \\ 13& 0& 2 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 2&18 &0 \\ 13& 0& 2 \end{bmatrix}$

$\begin{bmatrix} 6&6 &0 \\ 1& 0& 2 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 6&6 &0 \\ 1& 0& 2 \end{bmatrix}$

Not possible

$\begin{bmatrix} 6&18 &6 \\ 13& -22& 6 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 6&18 &6 \\ 13& -22& 6 \end{bmatrix}$

$\begin{bmatrix} 6&2 &0 \\ 1& 0& 6 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 6&2 &0 \\ 1& 0& 6 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 6&2 &0 \\ 1& 0& 6 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 6&2 &0 \\ 1& 0& 6 \end{bmatrix}$

Explanation:

In order to compute the sum of the two matrices, we need to sum up identical entries. This means we sum up $\displaystyle 4$, and $\displaystyle 2$, then $\displaystyle 10$, and $\displaystyle -8$, and etc. The computation in general looks like the following.

$\begin{bmatrix} a_1 & a_2 & a_3\\ b_1& b_2& b_3 \end{bmatrix} + \begin{bmatrix} c_1&c_2 &c_3 \\ d_1&d_2 & d_3 \end{bmatrix}=\begin{bmatrix} a_1+c_1& a_2+c_2 & a_3+c_3 \\ b_1+d_1& b_2+d_2 & b_3+d_3 \end{bmatrix}$ $\displaystyle \begin{bmatrix} a_1 & a_2 & a_3\\ b_1& b_2& b_3 \end{bmatrix} + \begin{bmatrix} c_1&c_2 &c_3 \\ d_1&d_2 & d_3 \end{bmatrix}=\begin{bmatrix} a_1+c_1& a_2+c_2 & a_3+c_3 \\ b_1+d_1& b_2+d_2 & b_3+d_3 \end{bmatrix}$

Apply this to our problem to get,

$\begin{bmatrix} 4 & 10 & -3\\ 7& -11& 4 \end{bmatrix} + \begin{bmatrix} 2&-8 &3 \\ -6&11 & 2 \end{bmatrix}=\begin{bmatrix} 4+2& 10+(-8) & -3+3 \\ 7+(-6)& -11+11 & 4+2 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 4 & 10 & -3\\ 7& -11& 4 \end{bmatrix} + \begin{bmatrix} 2&-8 &3 \\ -6&11 & 2 \end{bmatrix}=\begin{bmatrix} 4+2& 10+(-8) & -3+3 \\ 7+(-6)& -11+11 & 4+2 \end{bmatrix}$

$=\begin{bmatrix} 6&2 &0 \\ 1& 0& 6 \end{bmatrix}$ $\displaystyle =\begin{bmatrix} 6&2 &0 \\ 1& 0& 6 \end{bmatrix}$

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Example Question #214 : High School: Number And Quantity

Compute the sum of the two matrices.

$\begin{bmatrix} -2 & -3 & -3\\ -1& 6& 6 \end{bmatrix} + \begin{bmatrix} 2&2 &4 \\ 7&-11 & 7 \end{bmatrix}$ $\displaystyle \begin{bmatrix} -2 & -3 & -3\\ -1& 6& 6 \end{bmatrix} + \begin{bmatrix} 2&2 &4 \\ 7&-11 & 7 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 0&-1 &1 \\ 6& 5& 13 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 0&-1 &1 \\ 6& 5& 13 \end{bmatrix}$

$\begin{bmatrix} 0&-1 &1 \\ 6& -5& 13 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 0&-1 &1 \\ 6& -5& 13 \end{bmatrix}$

$\begin{bmatrix} 0&1 &1 \\ 6& -5& 13 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 0&1 &1 \\ 6& -5& 13 \end{bmatrix}$

$\begin{bmatrix} 0&-1 &1 \\ 6& -5& -13 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 0&-1 &1 \\ 6& -5& -13 \end{bmatrix}$

$\begin{bmatrix} 2&1 &1 \\ 6& -5& 13 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 2&1 &1 \\ 6& -5& 13 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 0&-1 &1 \\ 6& -5& 13 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 0&-1 &1 \\ 6& -5& 13 \end{bmatrix}$

Explanation:

In order to compute the sum of the two matrices, we need to sum up identical entries. This means we sum up $\displaystyle -2$, and $\displaystyle 2$, then $\displaystyle -3$, and $\displaystyle 2$, and etc. The computation in general looks like the following.

Apply this to our problem to get,

$\begin{bmatrix} -2 & -3 & -3\\ -1& 6& 6 \end{bmatrix} + \begin{bmatrix} 2&2 &4 \\ 7&-11 & 7 \end{bmatrix}=\begin{bmatrix} (-2)+2& (-3)+2 & (-3)+4 \\ (-1)+7& 6+(-11) & 6+7 \end{bmatrix}$ $\displaystyle \begin{bmatrix} -2 & -3 & -3\\ -1& 6& 6 \end{bmatrix} + \begin{bmatrix} 2&2 &4 \\ 7&-11 & 7 \end{bmatrix}=\begin{bmatrix} (-2)+2& (-3)+2 & (-3)+4 \\ (-1)+7& 6+(-11) & 6+7 \end{bmatrix}$

$=\begin{bmatrix} 0&-1 &1 \\ 6& -5& 13 \end{bmatrix}$ $\displaystyle =\begin{bmatrix} 0&-1 &1 \\ 6& -5& 13 \end{bmatrix}$

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Example Question #215 : High School: Number And Quantity

Compute the sum of the two matrices.

$\begin{bmatrix} -2 & -4 & 6\\ 5& -1& 2 \end{bmatrix} + \begin{bmatrix} -6&7 &0 \\ -5&-7 & 4 \end{bmatrix}$ $\displaystyle \begin{bmatrix} -2 & -4 & 6\\ 5& -1& 2 \end{bmatrix} + \begin{bmatrix} -6&7 &0 \\ -5&-7 & 4 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -8&3 &6 \\ 0& 8& 6 \end{bmatrix}$ $\displaystyle \begin{bmatrix} -8&3 &6 \\ 0& 8& 6 \end{bmatrix}$

$\begin{bmatrix} -8&3 &6 \\ 0& -8& 6 \end{bmatrix}$ $\displaystyle \begin{bmatrix} -8&3 &6 \\ 0& -8& 6 \end{bmatrix}$

$\begin{bmatrix} -8&3 &-6 \\ 0& -8& -6 \end{bmatrix}$ $\displaystyle \begin{bmatrix} -8&3 &-6 \\ 0& -8& -6 \end{bmatrix}$

$\begin{bmatrix} -8&-3 &6 \\ 0& -8& -6 \end{bmatrix}$ $\displaystyle \begin{bmatrix} -8&-3 &6 \\ 0& -8& -6 \end{bmatrix}$

$\begin{bmatrix} 8&3 &6 \\ 0& 8& 6 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 8&3 &6 \\ 0& 8& 6 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -8&3 &6 \\ 0& -8& 6 \end{bmatrix}$ $\displaystyle \begin{bmatrix} -8&3 &6 \\ 0& -8& 6 \end{bmatrix}$

Explanation:

In order to compute the sum of the two matrices, we need to sum up identical entries. This means we sum up $\displaystyle -2$, and $\displaystyle -6$, then $\displaystyle -4$, and $\displaystyle 7$, and etc. The computation in general looks like the following.

Apply this to our problem to get,

$\begin{bmatrix} -2 & -4 & 6\\ 5& -1& 2 \end{bmatrix} + \begin{bmatrix} -6&7 &0 \\ -5&-7 & 4 \end{bmatrix}=\begin{bmatrix} (-2)+(-6)& (-4)+7 & 6+0 \\ 5+(-5)& (-1)+(-7) & 2+4 \end{bmatrix}$ $\displaystyle \begin{bmatrix} -2 & -4 & 6\\ 5& -1& 2 \end{bmatrix} + \begin{bmatrix} -6&7 &0 \\ -5&-7 & 4 \end{bmatrix}=\begin{bmatrix} (-2)+(-6)& (-4)+7 & 6+0 \\ 5+(-5)& (-1)+(-7) & 2+4 \end{bmatrix}$

$=\begin{bmatrix} -8&3 &6 \\ 0& -8& 6 \end{bmatrix}$ $\displaystyle =\begin{bmatrix} -8&3 &6 \\ 0& -8& 6 \end{bmatrix}$

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Example Question #216 : High School: Number And Quantity

Compute the sum of the two matrices.

$\begin{bmatrix} 7 & -1 & 3\\ 3& -3& 2 \end{bmatrix} + \begin{bmatrix} 1&7 &0 \\ -2&5 & 2 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 7 & -1 & 3\\ 3& -3& 2 \end{bmatrix} + \begin{bmatrix} 1&7 &0 \\ -2&5 & 2 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 8&2 &3 \\ 1& 6& 4 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 8&2 &3 \\ 1& 6& 4 \end{bmatrix}$

$\begin{bmatrix} 8&6 &-3 \\ -1& 2& 4 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 8&6 &-3 \\ -1& 2& 4 \end{bmatrix}$

$\begin{bmatrix} 1&2 &3 \\ 8& 6& 4 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 1&2 &3 \\ 8& 6& 4 \end{bmatrix}$

$\begin{bmatrix} 8&-6 &3 \\ 1& 2& 0 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 8&-6 &3 \\ 1& 2& 0 \end{bmatrix}$

$\begin{bmatrix} 8&6 &3 \\ 1& 2& 4 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 8&6 &3 \\ 1& 2& 4 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 8&6 &3 \\ 1& 2& 4 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 8&6 &3 \\ 1& 2& 4 \end{bmatrix}$

Explanation:

In order to compute the sum of the two matrices, we need to sum up identical entries. This means we sum up $\displaystyle 7$, and $\displaystyle 1$, then $\displaystyle -1$, and $\displaystyle 7$, and etc. The computation in general looks like the following.

Apply this to our problem to get,

$\begin{bmatrix} 7 & -1 & 3\\ 3& -3& 2 \end{bmatrix} + \begin{bmatrix} 1&7 &0 \\ -2&5 & 2 \end{bmatrix}=\begin{bmatrix} 7+1& (-1)+7 & 3+0 \\ 3+(-2)& (-3)+5 & 2+2 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 7 & -1 & 3\\ 3& -3& 2 \end{bmatrix} + \begin{bmatrix} 1&7 &0 \\ -2&5 & 2 \end{bmatrix}=\begin{bmatrix} 7+1& (-1)+7 & 3+0 \\ 3+(-2)& (-3)+5 & 2+2 \end{bmatrix}$

$=\begin{bmatrix} 8&6 &3 \\ 1& 2& 4 \end{bmatrix}$ $\displaystyle =\begin{bmatrix} 8&6 &3 \\ 1& 2& 4 \end{bmatrix}$

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Example Question #1 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Compute the sum of the two matrices.

$\begin{bmatrix} 4 & 1 & 0\\ 5& 1&3 \end{bmatrix} + \begin{bmatrix} 5&0 &2 \\ 3&-2 & 5 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 4 & 1 & 0\\ 5& 1&3 \end{bmatrix} + \begin{bmatrix} 5&0 &2 \\ 3&-2 & 5 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 9&1 &8 \\ 8& -1& 2 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 9&1 &8 \\ 8& -1& 2 \end{bmatrix}$

$\begin{bmatrix} -9&1 &2 \\ 8& -1& 8 \end{bmatrix}$ $\displaystyle \begin{bmatrix} -9&1 &2 \\ 8& -1& 8 \end{bmatrix}$

$\begin{bmatrix} 9&1 &2 \\ 8& 1& 8 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 9&1 &2 \\ 8& 1& 8 \end{bmatrix}$

$\begin{bmatrix} 9&-1 &-2 \\ 8& -1& 8 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 9&-1 &-2 \\ 8& -1& 8 \end{bmatrix}$

$\begin{bmatrix} 9&1 &2 \\ 8& -1& 8 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 9&1 &2 \\ 8& -1& 8 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 9&1 &2 \\ 8& -1& 8 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 9&1 &2 \\ 8& -1& 8 \end{bmatrix}$

Explanation:

In order to compute the sum of the two matrices, we need to sum up identical entries. This means we sum up $\displaystyle 4$, and $\displaystyle 5$, then $\displaystyle 1$, and $\displaystyle 0$, and etc. The computation in general looks like the following.

Apply this to our problem to get,

$\begin{bmatrix} 4 & 1 & 0\\ 5& 1&3 \end{bmatrix} + \begin{bmatrix} 5&0 &2 \\ 3&-2 & 5 \end{bmatrix}=\begin{bmatrix} 4+5& 1+0 & 0+2 \\ 5+3& 1+(-2) & 3+5 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 4 & 1 & 0\\ 5& 1&3 \end{bmatrix} + \begin{bmatrix} 5&0 &2 \\ 3&-2 & 5 \end{bmatrix}=\begin{bmatrix} 4+5& 1+0 & 0+2 \\ 5+3& 1+(-2) & 3+5 \end{bmatrix}$

$=\begin{bmatrix} 9&1 &2 \\ 8& -1& 8 \end{bmatrix}$ $\displaystyle =\begin{bmatrix} 9&1 &2 \\ 8& -1& 8 \end{bmatrix}$

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Example Question #2 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Compute the sum of the two matrices.

$\begin{bmatrix} -2 & -4 & 6\\-4& -4& -5 \end{bmatrix} + \begin{bmatrix} 3&-1 &-4 \\ 7&6 & -4 \end{bmatrix}$ $\displaystyle \begin{bmatrix} -2 & -4 & 6\\-4& -4& -5 \end{bmatrix} + \begin{bmatrix} 3&-1 &-4 \\ 7&6 & -4 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 1&5 &2 \\ 3& 2& -9 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 1&5 &2 \\ 3& 2& -9 \end{bmatrix}$

$\begin{bmatrix} 1&-5 &-2 \\ -3& 2& -9 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 1&-5 &-2 \\ -3& 2& -9 \end{bmatrix}$

$\begin{bmatrix} 1&-5 &2 \\ 3& 2& -9 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 1&-5 &2 \\ 3& 2& -9 \end{bmatrix}$

$\begin{bmatrix} 1&5 &2 \\ 3& 2& 9 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 1&5 &2 \\ 3& 2& 9 \end{bmatrix}$

$\begin{bmatrix} 1&-5 &2 \\ 3& 2& 9 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 1&-5 &2 \\ 3& 2& 9 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 1&-5 &2 \\ 3& 2& -9 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 1&-5 &2 \\ 3& 2& -9 \end{bmatrix}$

Explanation:

In order to compute the sum of the two matrices, we need to sum up identical entries. This means we sum up $\displaystyle -2$, and $\displaystyle 3$, then $\displaystyle -4$, and $\displaystyle -1$, and etc. The computation in general looks like the following.

Apply this to our problem to get,

$\begin{bmatrix} -2 & -4 & 6\\-4& -4& -5 \end{bmatrix} + \begin{bmatrix} 3&-1 &-4 \\ 7&6 & -4 \end{bmatrix}=\begin{bmatrix} (-2)+3& (-4)+(-1) & 6+(-4) \\ (-4)+7& (-4)+6 & (-5)+(-4) \end{bmatrix}$ $\displaystyle \begin{bmatrix} -2 & -4 & 6\\-4& -4& -5 \end{bmatrix} + \begin{bmatrix} 3&-1 &-4 \\ 7&6 & -4 \end{bmatrix}=\begin{bmatrix} (-2)+3& (-4)+(-1) & 6+(-4) \\ (-4)+7& (-4)+6 & (-5)+(-4) \end{bmatrix}$

$=\begin{bmatrix} 1&-5 &2 \\ 3& 2& -9 \end{bmatrix}$ $\displaystyle =\begin{bmatrix} 1&-5 &2 \\ 3& 2& -9 \end{bmatrix}$

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Example Question #3 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Compute the sum of the two matrices.

$\begin{bmatrix} 1 & -4 & 3\\ 4& 1& 4 \end{bmatrix} + \begin{bmatrix} 3&-4 &-3 \\ 5&-1 & 2 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 1 & -4 & 3\\ 4& 1& 4 \end{bmatrix} + \begin{bmatrix} 3&-4 &-3 \\ 5&-1 & 2 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 4&-8 &0 \\ 9& 6& 0 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 4&-8 &0 \\ 9& 6& 0 \end{bmatrix}$

$\begin{bmatrix} 4&-8 &0 \\ 9& 0& 6 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 4&-8 &0 \\ 9& 0& 6 \end{bmatrix}$

$\begin{bmatrix} 4&0 &0 \\ 9& -8& 6 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 4&0 &0 \\ 9& -8& 6 \end{bmatrix}$

$\begin{bmatrix} 4&8 &0 \\ 9& 0& 6 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 4&8 &0 \\ 9& 0& 6 \end{bmatrix}$

$\begin{bmatrix} 4&-8 &0 \\ 0& 9& 6 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 4&-8 &0 \\ 0& 9& 6 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 4&-8 &0 \\ 9& 0& 6 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 4&-8 &0 \\ 9& 0& 6 \end{bmatrix}$

Explanation:

In order to compute the sum of the two matrices, we need to sum up identical entries. This means we sum up $\displaystyle 1$, and $\displaystyle 3$, then $\displaystyle -4$, and $\displaystyle -4$, and etc. The computation in general looks like the following.

Apply this to our problem to get,

$\begin{bmatrix} 1 & -4 & 3\\ 4& 1& 4 \end{bmatrix} + \begin{bmatrix} 3&-4 &-3 \\ 5&-1 & 2 \end{bmatrix}=\begin{bmatrix} 1+3& (-4)+(-4) & 3+(-3) \\ 4+5& 1+(-1) & 4+2 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 1 & -4 & 3\\ 4& 1& 4 \end{bmatrix} + \begin{bmatrix} 3&-4 &-3 \\ 5&-1 & 2 \end{bmatrix}=\begin{bmatrix} 1+3& (-4)+(-4) & 3+(-3) \\ 4+5& 1+(-1) & 4+2 \end{bmatrix}$

$=\begin{bmatrix} 4&-8 &0 \\ 9& 0& 6 \end{bmatrix}$ $\displaystyle =\begin{bmatrix} 4&-8 &0 \\ 9& 0& 6 \end{bmatrix}$

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Example Question #4 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Compute the sum of the two matrices.

$\begin{bmatrix} 0 & -3 & -3\\ -4& -3& -2 \end{bmatrix} + \begin{bmatrix} 4&-5 &-1 \\ -1&-5 & 0 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 0 & -3 & -3\\ -4& -3& -2 \end{bmatrix} + \begin{bmatrix} 4&-5 &-1 \\ -1&-5 & 0 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 4&8 &4 \\ 5& 8& 2 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 4&8 &4 \\ 5& 8& 2 \end{bmatrix}$

$\begin{bmatrix} 4&8 &-4 \\ -5& -8& -2 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 4&8 &-4 \\ -5& -8& -2 \end{bmatrix}$

$\begin{bmatrix} 4&8 &-4 \\ -5& 8& -2 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 4&8 &-4 \\ -5& 8& -2 \end{bmatrix}$

$\begin{bmatrix} 4&-8 &-4 \\ -5& -8& -2 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 4&-8 &-4 \\ -5& -8& -2 \end{bmatrix}$

$\begin{bmatrix} 4&-8 &-2 \\ -5& -8& -4 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 4&-8 &-2 \\ -5& -8& -4 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 4&-8 &-4 \\ -5& -8& -2 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 4&-8 &-4 \\ -5& -8& -2 \end{bmatrix}$

Explanation:

In order to compute the sum of the two matrices, we need to sum up identical entries. This means we sum up $\displaystyle 0$, and $\displaystyle 4$, then $\displaystyle -3$, and $\displaystyle -5$, and etc. The computation in general looks like the following.

Apply this to our problem to get,

$\begin{bmatrix} 0 & -3 & -3\\ -4& -3& -2 \end{bmatrix} + \begin{bmatrix} 4&-5 &-1 \\ -1&-5 & 0 \end{bmatrix}=\begin{bmatrix} 0+4& -3+(-5) & (-3)+(-1) \\ (-4)+(-1)& (-3)+(-5) & (-2)+0 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 0 & -3 & -3\\ -4& -3& -2 \end{bmatrix} + \begin{bmatrix} 4&-5 &-1 \\ -1&-5 & 0 \end{bmatrix}=\begin{bmatrix} 0+4& -3+(-5) & (-3)+(-1) \\ (-4)+(-1)& (-3)+(-5) & (-2)+0 \end{bmatrix}$

$=\begin{bmatrix} 4&-8 &-4 \\ -5& -8& -2 \end{bmatrix}$ $\displaystyle =\begin{bmatrix} 4&-8 &-4 \\ -5& -8& -2 \end{bmatrix}$

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Example Question #121 : Vector & Matrix Quantities

Compute the sum of the two matrices.

$\begin{bmatrix} 5 & 0 & -5\\ -5& 3& -1 \end{bmatrix} + \begin{bmatrix} 6&-2 &-5 \\ -5&5 & -4 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 5 & 0 & -5\\ -5& 3& -1 \end{bmatrix} + \begin{bmatrix} 6&-2 &-5 \\ -5&5 & -4 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 11&-2 &-10 \\ -10& 8& -5 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 11&-2 &-10 \\ -10& 8& -5 \end{bmatrix}$

$\begin{bmatrix} -11&-2 &-10 \\ -10& 8& -5 \end{bmatrix}$ $\displaystyle \begin{bmatrix} -11&-2 &-10 \\ -10& 8& -5 \end{bmatrix}$

$\begin{bmatrix} 11&-2 &10 \\ -10& 8& 5 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 11&-2 &10 \\ -10& 8& 5 \end{bmatrix}$

$\begin{bmatrix} 11&-2 &10 \\ 10& 8& -5 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 11&-2 &10 \\ 10& 8& -5 \end{bmatrix}$

$\begin{bmatrix} 11&2 &-10 \\ -10& 8& -5 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 11&2 &-10 \\ -10& 8& -5 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 11&-2 &-10 \\ -10& 8& -5 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 11&-2 &-10 \\ -10& 8& -5 \end{bmatrix}$

Explanation:

In order to compute the sum of the two matrices, we need to sum up identical entries. This means we sum up $\displaystyle 5$, and $\displaystyle 6$, then $\displaystyle 0$, and $\displaystyle -2$, and etc. The computation in general looks like the following.

Apply this to our problem to get,

$\begin{bmatrix} 5 & 0 & -5\\ -5& 3& -1 \end{bmatrix} + \begin{bmatrix} 6&-2 &-5 \\ -5&5 & -4 \end{bmatrix}=\begin{bmatrix} 5+6& 0+(-2) & (-5)+(-5) \\ (-5)+(-5)& 3+5 & (-1)+(-4) \end{bmatrix}$ $\displaystyle \begin{bmatrix} 5 & 0 & -5\\ -5& 3& -1 \end{bmatrix} + \begin{bmatrix} 6&-2 &-5 \\ -5&5 & -4 \end{bmatrix}=\begin{bmatrix} 5+6& 0+(-2) & (-5)+(-5) \\ (-5)+(-5)& 3+5 & (-1)+(-4) \end{bmatrix}$

$=\begin{bmatrix} 11&-2 &-10 \\ -10& 8& -5 \end{bmatrix}$ $\displaystyle =\begin{bmatrix} 11&-2 &-10 \\ -10& 8& -5 \end{bmatrix}$

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Example Question #122 : Vector & Matrix Quantities

Compute the sum of the two matrices.

$\begin{bmatrix} 3 & -2 & 5\\ -3& -5& 5 \end{bmatrix} + \begin{bmatrix} 7&0 &0 \\ -4&2 & -2 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 3 & -2 & 5\\ -3& -5& 5 \end{bmatrix} + \begin{bmatrix} 7&0 &0 \\ -4&2 & -2 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 10&-2 &5 \\ -7& -3& 3 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 10&-2 &5 \\ -7& -3& 3 \end{bmatrix}$

$\begin{bmatrix} 10&-2 &3 \\ -7& -3& 5 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 10&-2 &3 \\ -7& -3& 5 \end{bmatrix}$

$\begin{bmatrix} 10&2 &5 \\ 7& 3& 3 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 10&2 &5 \\ 7& 3& 3 \end{bmatrix}$

$\begin{bmatrix} 10&-2 &5 \\ 7& -3& 3 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 10&-2 &5 \\ 7& -3& 3 \end{bmatrix}$

$\begin{bmatrix} 10&-2 &5 \\ -7& 3& 3 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 10&-2 &5 \\ -7& 3& 3 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 10&-2 &5 \\ -7& -3& 3 \end{bmatrix}$ $\displaystyle \begin{bmatrix} 10&-2 &5 \\ -7& -3& 3 \end{bmatrix}$

Explanation:

In order to compute the sum of the two matrices, we need to sum up identical entries. This means we sum up $\displaystyle 3$, and $\displaystyle 7$, then $\displaystyle -2$, and $\displaystyle 0$, and etc. The computation in general looks like the following.

Apply this to our problem to get,

$\begin{bmatrix} 3 & -2 & 5\\ -3& -5& 5 \end{bmatrix} + \begin{bmatrix} 7&0 &0 \\ -4&2 & -2 \end{bmatrix}=\begin{bmatrix} 3+7& (-2)+0 & 5+0 \\ (-3)+(-4)& (-5)+2 & 5+(-2) \end{bmatrix}$ $\displaystyle \begin{bmatrix} 3 & -2 & 5\\ -3& -5& 5 \end{bmatrix} + \begin{bmatrix} 7&0 &0 \\ -4&2 & -2 \end{bmatrix}=\begin{bmatrix} 3+7& (-2)+0 & 5+0 \\ (-3)+(-4)& (-5)+2 & 5+(-2) \end{bmatrix}$

$=\begin{bmatrix} 10&-2 &5 \\ -7& -3& 3 \end{bmatrix}$ $\displaystyle =\begin{bmatrix} 10&-2 &5 \\ -7& -3& 3 \end{bmatrix}$

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If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

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Contact Information

* Full legal name

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Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

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Common Core: High School - Number and Quantity : Matrices Operations (Add, Subtract, and Multiply): CCSS.Math.Content.HSN-VM.C.8

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

All Common Core: High School - Number and Quantity Resources

Example Questions

Example Question #213 : High School: Number And Quantity

Example Question #214 : High School: Number And Quantity

Example Question #215 : High School: Number And Quantity

Example Question #216 : High School: Number And Quantity

Example Question #1 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Example Question #2 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Example Question #3 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Example Question #4 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Example Question #121 : Vector & Matrix Quantities

Example Question #122 : Vector & Matrix Quantities

All Common Core: High School - Number and Quantity Resources

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