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Common Core: High School - Number and Quantity : Vector & Matrix Quantities

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

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All Common Core: High School - Number and Quantity Resources

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Example Questions

Example Question #196 : High School: Number And Quantity

Which of the following matrices represents the equations, 1:-18x-6y=4 , and 2:-4x-7y=15 ?

Possible Answers:

$\begin{bmatrix} -18 & -7 &4 \\ -4& -6& 15\end{bmatrix}$

$\begin{bmatrix} -18 & -6 &4 \\ -4& -7& 15\end{bmatrix}$

$\begin{bmatrix} -18 & -6 &-4 \\ -4& -7& -15\end{bmatrix}$

$\begin{bmatrix} 18 & 6 &4 \\ 4& 7& 15\end{bmatrix}$

$\begin{bmatrix} 18 & -6 &4 \\ -4& 7& 15\end{bmatrix}$

Correct answer:

$\begin{bmatrix} -18 & -6 &4 \\ -4& -7& 15\end{bmatrix}$

Explanation:

To do this problem, all we need to do is put the coefficients for each variable into a matrix. The first column will be x values, 2nd column will be y values, and 3rd column will be what the equations are equal to.

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \\ x_2& y_2& c_2 \end{bmatrix}$

where x_1,y_1 , x_2,y_2 are coefficients of and in the first and second equation respectively. c_1, c_2 refer to what the equations are equal to. So after placing the coefficients and what the equations are equal to in a matrix, it will look like the following.

$\begin{bmatrix} -18 & -6 &4 \\ -4& -7& 15\end{bmatrix}$

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Example Question #197 : High School: Number And Quantity

Which of the following matrices represents the equations, 1:-18x+8y=-9 , and 2:8x+6y=11 ?

Possible Answers:

$\begin{bmatrix} 18 & 8 &-9 \\ 8& 6& 11 \end{bmatrix}$

$\begin{bmatrix} -18 & 8 &-9 \\ 8& 6& 11 \end{bmatrix}$

$\begin{bmatrix} 18 & 8 &9 \\ 8& 6& 11 \end{bmatrix}$

$\begin{bmatrix} -18 & 8 &9 \\ 8& 6& 11 \end{bmatrix}$

$\begin{bmatrix} -18 & 6 &-9 \\ 8& 8& 11 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -18 & 8 &-9 \\ 8& 6& 11 \end{bmatrix}$

Explanation:

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \\ x_2& y_2& c_2 \end{bmatrix}$

$\begin{bmatrix} -18 & 8 &-9 \\ 8& 6& 11 \end{bmatrix}$

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Example Question #198 : High School: Number And Quantity

Which of the following matrices represents the equations, 1:11x-15y=16 , and 2:-14x+20y=-18 ?

Possible Answers:

$\begin{bmatrix} 11 & 15 &16 \\ 14& 20& -18\end{bmatrix}$

$\begin{bmatrix} 11 & -15 &16 \\ -14& 20& 18\end{bmatrix}$

$\begin{bmatrix} 11 & 15 &16 \\ 14& 20& 18\end{bmatrix}$

$\begin{bmatrix} 11 & -15 &16 \\ -14& 20& -18\end{bmatrix}$

$\begin{bmatrix} -11 & -15 &-16 \\ -14& -20& -18\end{bmatrix}$

Correct answer:

$\begin{bmatrix} 11 & -15 &16 \\ -14& 20& -18\end{bmatrix}$

Explanation:

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \\ x_2& y_2& c_2 \end{bmatrix}$

$\begin{bmatrix} 11 & -15 &16 \\ -14& 20& -18\end{bmatrix}$

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Example Question #199 : High School: Number And Quantity

Which of the following matrices represents the equations, 1:19x-8y=-20 , and 2:17x+4y=20 ?

Possible Answers:

$\begin{bmatrix} 19 & -8 &-20 \\ -17& 4& -20 \end{bmatrix}$

$\begin{bmatrix} -19 & -8 &-20 \\ 17& -4& 20 \end{bmatrix}$

$\begin{bmatrix} 19 & -8 &-20 \\ 17& 4& 20 \end{bmatrix}$

$\begin{bmatrix} 19 & -8 &-20 \\ -17& -4& -20 \end{bmatrix}$

$\begin{bmatrix} -19 & 8 &20 \\ 17& -4& 20 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 19 & -8 &-20 \\ 17& 4& 20 \end{bmatrix}$

Explanation:

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \\ x_2& y_2& c_2 \end{bmatrix}$

$\begin{bmatrix} 19 & -8 &-20 \\ 17& 4& 20 \end{bmatrix}$

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Example Question #2 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Which of the following matrices represents the equations, 1:-10x+4y=9 , and 2:-x+16y=4 ?

Possible Answers:

$\begin{bmatrix} -10 & 4 &-9 \\ -1& -16& 4 \end{bmatrix}$

$\begin{bmatrix} 10 & 4 &9 \\ -1& 16& 4 \end{bmatrix}$

$\begin{bmatrix} -10 & 4 &9 \\ -1& 16& 4 \end{bmatrix}$

$\begin{bmatrix} -10 & -4 &9 \\ -1& -16& 4 \end{bmatrix}$

$\begin{bmatrix} -10 & 4 &9 \\ -1& 16& -4 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -10 & 4 &9 \\ -1& 16& 4 \end{bmatrix}$

Explanation:

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \\ x_2& y_2& c_2 \end{bmatrix}$

$\begin{bmatrix} -10 & 4 &9 \\ -1& 16& 4 \end{bmatrix}$

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Example Question #1 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Which of the following matrices represents the equations, 1:-14x-y=-6 , and 2:14x+18y=17 ?

Possible Answers:

$\begin{bmatrix} -14 & -1 &-6 \\ -14& -18& -17 \end{bmatrix}$

$\begin{bmatrix} -14 & -1 &-6 \\ -14& 18& -17 \end{bmatrix}$

$\begin{bmatrix} -14 & -1 &-6 \\ 14& 18& 17 \end{bmatrix}$

$\begin{bmatrix} 14 & 1 &6 \\ 14& 18& 17 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -14 & -1 &-6 \\ 14& 18& 17 \end{bmatrix}$

Explanation:

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \\ x_2& y_2& c_2 \end{bmatrix}$

$\begin{bmatrix} -14 & -1 &-6 \\ 14& 18& 17 \end{bmatrix}$

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Example Question #11 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Which of the following matrices represents the equations, 1:10x-14y=-17 , and 2:-9x+18y=-12 ?

Possible Answers:

$\begin{bmatrix} 10 & -14 &-17 \\ -9& 18& -12 \end{bmatrix}$

$\begin{bmatrix} 10 & 14 &17 \\ 9& 18& -12 \end{bmatrix}$

$\begin{bmatrix} 10 & 14 &-17 \\ 9& 18& -12 \end{bmatrix}$

$\begin{bmatrix} -10 & -14 &-17 \\ -9& 18& -12 \end{bmatrix}$

$\begin{bmatrix} -10 & -14 &-17 \\ -9& -18& -12 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 10 & -14 &-17 \\ -9& 18& -12 \end{bmatrix}$

Explanation:

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \\ x_2& y_2& c_2 \end{bmatrix}$

$\begin{bmatrix} 10 & -14 &-17 \\ -9& 18& -12 \end{bmatrix}$

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Example Question #12 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Which of the following matrices represents the equations, 1:-x-14y=-1 , and 2:-5x+8y=9 ?

Possible Answers:

$\begin{bmatrix} -1 & -14 &-11 \\ -5& 8& 9 \end{bmatrix}$

$\begin{bmatrix}0 & -1 &-1 \\ -5& 8& 9 \end{bmatrix}$

$\begin{bmatrix} -1 & -14 &1 \\ -5& 8& 9 \end{bmatrix}$

$\begin{bmatrix} 0 & -14 &-1 \\ -5& 8& 9 \end{bmatrix}$

$\begin{bmatrix} -1 & -14 &-1 \\ -5& 8& 9 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -1 & -14 &-1 \\ -5& 8& 9 \end{bmatrix}$

Explanation:

It will look like this

$\begin{bmatrix} x_1 & y_1 &c_1 \\ x_2& y_2& c_2 \end{bmatrix}$

$\begin{bmatrix} -1 & -14 &-1 \\ -5& 8& 9 \end{bmatrix}$

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Example Question #1 : Multiply Matrices By Scalar: Ccss.Math.Content.Hsn Vm.C.7

Compute

$3\begin{bmatrix} 2 & 4&-2 \\ 1&20 &-4 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 6 & 12&-6 \\ 3&60 &-12 \end{bmatrix}$

$\begin{bmatrix} 5 & 7&1 \\ 4&23 &-1 \end{bmatrix}$

$\begin{bmatrix} 10 & 13&-8 \\ 3&60 &-12 \end{bmatrix}$

Not possible

Correct answer:

$\begin{bmatrix} 6 & 12&-6 \\ 3&60 &-12 \end{bmatrix}$

Explanation:

In order to compute this, we need to multiply each entry by the scalar .

$3\begin{bmatrix} 2 & 4&-2 \\ 1&20 &-4 \end{bmatrix}=\begin{bmatrix} 2\cdot3 & 4\cdot3&-2\cdot3 \\ 1\cdot3&20\cdot3 &-4\cdot3 \end{bmatrix}=\begin{bmatrix} 6 & 12&-6 \\ 3&60 &-12 \end{bmatrix}$

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Example Question #2 : Multiply Matrices By Scalar: Ccss.Math.Content.Hsn Vm.C.7

Compute

$5\begin{bmatrix} 20 & 4&-3 \\ 2&14 &-1 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 100 & 20&-15 \\ 10&70 &-5 \end{bmatrix}$

$\begin{bmatrix} 100 & 20&15 \\ 10&70 &5 \end{bmatrix}$

$\begin{bmatrix} 100 & -20&-15 \\ -10&70 &-5 \end{bmatrix}$

$\begin{bmatrix} -100 & -20&-15 \\ 10&70 &-5 \end{bmatrix}$

$\begin{bmatrix} -100 & -20&-15 \\ -10&-70 &-5 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 100 & 20&-15 \\ 10&70 &-5 \end{bmatrix}$

Explanation:

In order to compute this, we need to multiply each entry by the scalar .

$5\begin{bmatrix} 20 & 4&-3 \\ 2&14 &-1 \end{bmatrix}=\begin{bmatrix} 5\cdot20 & 5\cdot4&5\cdot(-3) \\ 5\cdot2&5\cdot14 &5\cdot(-1) \end{bmatrix}=\begin{bmatrix} 100 & 20&-15 \\ 10&70 &-5 \end{bmatrix}$

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All Common Core: High School - Number and Quantity Resources

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Common Core: High School - Number and Quantity : Vector & Matrix Quantities

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 #196 : High School: Number And Quantity

Example Question #197 : High School: Number And Quantity

Example Question #198 : High School: Number And Quantity

Example Question #199 : High School: Number And Quantity

Example Question #2 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Example Question #1 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Example Question #11 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Example Question #12 : Use Matrices To Represent And Manipulate Data: Ccss.Math.Content.Hsn Vm.C.6

Example Question #1 : Multiply Matrices By Scalar: Ccss.Math.Content.Hsn Vm.C.7

Example Question #2 : Multiply Matrices By Scalar: Ccss.Math.Content.Hsn Vm.C.7

All Common Core: High School - Number and Quantity Resources

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