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Common Core: High School - Number and Quantity : High School: Number and Quantity

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 #2 : Vector Multiplication (Matrices Being Transformations Of Vectors): Ccss.Math.Content.Hsn Vm.C.11

Calculate

$\begin{bmatrix} 5&-11 \\ -3& 13 \end{bmatrix} \times \begin{bmatrix} -1\\ 13 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -148\\ -172 \end{bmatrix}$

$\begin{bmatrix} 148\\ 172 \end{bmatrix}$

$\begin{bmatrix} 148\\ -172 \end{bmatrix}$

$\begin{bmatrix} -148\\ 172 \end{bmatrix}$

$\begin{bmatrix} 172\\-148 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -148\\ 172 \end{bmatrix}$

Explanation:

In order to do matrix multiplication, we need to check if the dimensions check out. The matrix on the left is $2\times2$ , and the matrix on the right is $2\times1$ , so the dimensions check out. The resulting matrix will be $2\times1$ . To do matrix multiplication, we take the rows of the matrix on the left, and multiply by the columns of the right matrix. Then we sum the results together. This is what it looks like in general.

$\begin{bmatrix} a& b\\ c& d \end{bmatrix} \times \begin{bmatrix} e\\ f \end{bmatrix} = \begin{bmatrix} a\cdot e+b\cdot f\\ c\cdot e+d\cdot f \end{bmatrix}$

Now we apply the above to get the following solution.

$\begin{bmatrix} 5&-11 \\ -3& 13 \end{bmatrix} \times \begin{bmatrix} -1\\ 13 \end{bmatrix}=\begin{bmatrix} 5\cdot(-1)+(-11)\cdot13\\ (-3)\cdot (-1)+13\cdot13 \end{bmatrix} =\begin{bmatrix} -5-143\\ 3+169 \end{bmatrix} =\begin{bmatrix} -148\\ 172 \end{bmatrix}$

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Example Question #1 : Vector Multiplication (Matrices Being Transformations Of Vectors): Ccss.Math.Content.Hsn Vm.C.11

Calculate

$\begin{bmatrix} 18&-13 \\ 6& -2 \end{bmatrix} \times \begin{bmatrix} 10\\ -13 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -349\\ -86 \end{bmatrix}$

$\begin{bmatrix} 349\\ -86 \end{bmatrix}$

$\begin{bmatrix} 349\\ 86 \end{bmatrix}$

$\begin{bmatrix} -349\\ 86 \end{bmatrix}$

$\begin{bmatrix} 86\\349 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 349\\ 86 \end{bmatrix}$

Explanation:

$\begin{bmatrix} a& b\\ c& d \end{bmatrix} \times \begin{bmatrix} e\\ f \end{bmatrix} = \begin{bmatrix} a\cdot e+b\cdot f\\ c\cdot e+d\cdot f \end{bmatrix}$

Now we apply the above to get the following solution.

$\begin{bmatrix} 18&-13 \\ 6& -2 \end{bmatrix} \times \begin{bmatrix} 10\\ -13 \end{bmatrix}=\begin{bmatrix} 18\cdot10+(-13)\cdot(-13)\\ 6\cdot 10+(-2)\cdot(-13) \end{bmatrix} =\begin{bmatrix} 180+169\\ 60+26 \end{bmatrix} =\begin{bmatrix} 349\\ 86 \end{bmatrix}$

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Example Question #162 : Vector & Matrix Quantities

Calculate

$\begin{bmatrix} 16&-20 \\ -15& -1 \end{bmatrix} \times \begin{bmatrix} 15\\ -2 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -223\\280 \end{bmatrix}$

$\begin{bmatrix} 280\\ -223 \end{bmatrix}$

$\begin{bmatrix} 280\\ 223 \end{bmatrix}$

$\begin{bmatrix} -280\\ 223 \end{bmatrix}$

$\begin{bmatrix} -280\\ -223 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 280\\ -223 \end{bmatrix}$

Explanation:

$\begin{bmatrix} a& b\\ c& d \end{bmatrix} \times \begin{bmatrix} e\\ f \end{bmatrix} = \begin{bmatrix} a\cdot e+b\cdot f\\ c\cdot e+d\cdot f \end{bmatrix}$

Now we apply the above to get the following solution.

$\begin{bmatrix} 16&-20 \\ -15& -1 \end{bmatrix} \times \begin{bmatrix} 15\\ -2 \end{bmatrix}=\begin{bmatrix} 16\cdot15+(-20)\cdot(-2)\\ (-15)\cdot 15+(-1)\cdot(-2) \end{bmatrix} =\begin{bmatrix} 240+40\\ -225+2 \end{bmatrix} =\begin{bmatrix} 280\\ -223 \end{bmatrix}$

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Example Question #163 : Vector & Matrix Quantities

Calculate

$\begin{bmatrix} -5&8 \\ -8& -5 \end{bmatrix} \times \begin{bmatrix} -15\\ 10 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -70 \\155\\ \end{bmatrix}$

$\begin{bmatrix} 70 \\155\\ \end{bmatrix}$

$\begin{bmatrix} 155\\ 70 \end{bmatrix}$

$\begin{bmatrix} 155\\ -70 \end{bmatrix}$

$\begin{bmatrix} -155\\ 70 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 155\\ 70 \end{bmatrix}$

Explanation:

$\begin{bmatrix} a& b\\ c& d \end{bmatrix} \times \begin{bmatrix} e\\ f \end{bmatrix} = \begin{bmatrix} a\cdot e+b\cdot f\\ c\cdot e+d\cdot f \end{bmatrix}$

Now we apply the above to get the following solution.

$\begin{bmatrix} -5&8 \\ -8& -5 \end{bmatrix} \times \begin{bmatrix} -15\\ 10 \end{bmatrix}=\begin{bmatrix} (-5)\cdot(-15)+8\cdot10\\ (-8)\cdot (-15)+(-5)\cdot10 \end{bmatrix} =\begin{bmatrix} 75+80\\ 120-50 \end{bmatrix} =\begin{bmatrix} 155\\ 70 \end{bmatrix}$

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Example Question #261 : High School: Number And Quantity

What is the determinant of the following matrix?

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

Possible Answers:

$\uptext{determinant}=5$

$\uptext{determinant}=9$

$\uptext{determinant}=15$

$\uptext{determinant}=13$

$\uptext{determinant}=1$

Correct answer:

$\uptext{determinant}=13$

Explanation:

To find the determinant of the matrix, we need to multiply the main diagonal entries together, then multiply the off diagonal entries and then find the difference between them. It looks like the following.

$\det\left( {\begin{bmatrix} a &b \\ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=3\cdot3-(-4)(1)=9-(-4)=9+4=13$

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Example Question #262 : High School: Number And Quantity

What is the determinant of the following matrix?

$\begin{bmatrix} 24&3 \\ -12& 8 \end{bmatrix}$

Possible Answers:

$\uptext{determinant}=228$

$\uptext{determinant}=-228$

$\uptext{determinant}=0$

$\uptext{determinant}=28$

$\uptext{determinant}=22$

Correct answer:

$\uptext{determinant}=228$

Explanation:

$\det\left( {\begin{bmatrix} a &b \\ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=24\cdot8-(3)(-12)=192-(-36)=192+36=228$

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Example Question #171 : Vector & Matrix Quantities

What is the determinant of the following matrix?

$\begin{bmatrix} -4&-16 \\ 4& -16 \end{bmatrix}$

Possible Answers:

$\uptext{determinant}=64$

$\uptext{determinant}=0$

$\uptext{determinant}=1$

$\uptext{determinant}=128$

$\uptext{determinant}=12$

Correct answer:

$\uptext{determinant}=128$

Explanation:

$\det\left( {\begin{bmatrix} a &b \\ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=-4\cdot-16-(-16)(4)=64-(-64)=64+64=128$

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Example Question #4 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

What is the determinant of the following matrix?

$\begin{bmatrix} -6&8 \\ 24& -18 \end{bmatrix}$

Possible Answers:

$\uptext{determinant}=1$

$\uptext{determinant}=-8$

$\uptext{determinant}=-84$

$\uptext{determinant}=-60$

$\uptext{determinant}=84$

Correct answer:

$\uptext{determinant}=-84$

Explanation:

$\det\left( {\begin{bmatrix} a &b \\ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=-6\cdot(-18)-(8)(24)=108-192=-84$

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Example Question #5 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

What is the determinant of the following matrix?

$\begin{bmatrix} 2&-10 \\ -12& 21 \end{bmatrix}$

Possible Answers:

$\uptext{determinant}=-8$

$\uptext{determinant}=-78$

$\uptext{determinant}=-7$

$\uptext{determinant}=78$

$\uptext{determinant}=0$

Correct answer:

$\uptext{determinant}=-78$

Explanation:

$\det\left( {\begin{bmatrix} a &b \\ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=2\cdot21-(-10)(-12)=42-120=-78$

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Example Question #6 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

What is the determinant of the following matrix?

$\begin{bmatrix} 4&1 \\ -6& -28 \end{bmatrix}$

Possible Answers:

$\uptext{determinant}=-106$

$\uptext{determinant}=106$

$\uptext{determinant}=-1$

$\uptext{determinant}=-16$

$\uptext{determinant}=-10$

Correct answer:

$\uptext{determinant}=-106$

Explanation:

$\det\left( {\begin{bmatrix} a &b \\ c& d \end{bmatrix}} \right) =ad-bc$

We apply this to our problem to get

$\uptext{determinant}=4\cdot(-28)-(1)(-6)=-112+6=-106$

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Common Core: High School - Number and Quantity : High School: Number and Quantity

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 #2 : Vector Multiplication (Matrices Being Transformations Of Vectors): Ccss.Math.Content.Hsn Vm.C.11

Example Question #1 : Vector Multiplication (Matrices Being Transformations Of Vectors): Ccss.Math.Content.Hsn Vm.C.11

Example Question #162 : Vector & Matrix Quantities

Example Question #163 : Vector & Matrix Quantities

Example Question #261 : High School: Number And Quantity

Example Question #262 : High School: Number And Quantity

Example Question #171 : Vector & Matrix Quantities

Example Question #4 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

Example Question #5 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

Example Question #6 : Interpret The Absolute Value Of The Determinant Of A 2 By 2 Matrix: Ccss.Math.Content.Hsn Vm.C.12

All Common Core: High School - Number and Quantity Resources

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