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Common Core: High School - Number and Quantity : Vector Multiplication (Matrices being Transformations of Vectors): CCSS.Math.Content.HSN-VM.C.11

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Example Questions

Example Question #151 : Vector & Matrix Quantities

Calculate

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

Possible Answers:

$\begin{bmatrix} 3 & 4\\ 2 & 4 \end{bmatrix}$

$\begin{bmatrix} 7\\ 2 \end{bmatrix}$

$\begin{bmatrix} 5\\ 11 \end{bmatrix}$

$\begin{bmatrix} 11\\ 5 \end{bmatrix}$

Not possible

Correct answer:

$\begin{bmatrix} 11\\ 5 \end{bmatrix}$

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.

$\begin{bmatrix} 3&4 \\ 1& 2 \end{bmatrix} \times \begin{bmatrix} 1\\ 2 \end{bmatrix}=\begin{bmatrix} 3\cdot1+4\cdot2\\ 1\cdot 1+2\cdot2 \end{bmatrix} =\begin{bmatrix} 3+8\\ 1+4 \end{bmatrix} =\begin{bmatrix} 11\\ 5 \end{bmatrix}$

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

Calculate

$\begin{bmatrix} 17&14 \\ 4& -19 \end{bmatrix} \times \begin{bmatrix} 10\\ -16 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -54\\ -344 \end{bmatrix}$

$\begin{bmatrix} 54\\ 344 \end{bmatrix}$

$\begin{bmatrix} -344\\ 54 \end{bmatrix}$

$\begin{bmatrix} 344\\ 54 \end{bmatrix}$

$\begin{bmatrix} -54\\ 344 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -54\\ 344 \end{bmatrix}$

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.

$\begin{bmatrix} 17&14 \\ 4& -19 \end{bmatrix} \times \begin{bmatrix} 10\\ -16 \end{bmatrix}=\begin{bmatrix} 17\cdot10+14\cdot-16\\ 4\cdot 10+(-19)\cdot(-16) \end{bmatrix} =\begin{bmatrix} 170-224\\ 40+304 \end{bmatrix} =\begin{bmatrix} -54\\ 344 \end{bmatrix}$

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Example Question #152 : Vector & Matrix Quantities

Calculate

$\begin{bmatrix} 7&-1 \\ -16& -1 \end{bmatrix} \times \begin{bmatrix} 17\\ 3 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 116\\ -275 \end{bmatrix}$

$\begin{bmatrix} 116\\ 275 \end{bmatrix}$

$\begin{bmatrix} -116\\ -275 \end{bmatrix}$

$\begin{bmatrix} -275\\ 116 \end{bmatrix}$

$\begin{bmatrix} -275\\ -116 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 116\\ -275 \end{bmatrix}$

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.

$\begin{bmatrix} 7&-1 \\ -16& -1 \end{bmatrix} \times \begin{bmatrix} 17\\ 3 \end{bmatrix}=\begin{bmatrix} 7\cdot17+(-1)\cdot3\\ (-16)\cdot 17+(-1)\cdot3 \end{bmatrix} =\begin{bmatrix} 119-3\\ -272-3 \end{bmatrix} =\begin{bmatrix} 116\\ -275 \end{bmatrix}$

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Example Question #4 : Vector Multiplication (Matrices Being Transformations Of Vectors): Ccss.Math.Content.Hsn Vm.C.11

Calculate

$\begin{bmatrix} -2&-19 \\ 9& 5 \end{bmatrix} \times \begin{bmatrix} -12\\ 10 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -166\\ 58 \end{bmatrix}$

$\begin{bmatrix} 166\\ 58 \end{bmatrix}$

$\begin{bmatrix} 166\\ -58 \end{bmatrix}$

$\begin{bmatrix} -58\\ -166 \end{bmatrix}$

$\begin{bmatrix} -166\\ -58 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -166\\ -58 \end{bmatrix}$

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.

$\\ \begin{bmatrix} -2&-19 \\ 9& 5 \end{bmatrix} \times \begin{bmatrix} -12\\ 10 \end{bmatrix}=\begin{bmatrix}(-2)\cdot(-12)+(-19)\cdot10\\ 9\cdot (-12)+5\cdot10 \end{bmatrix} =\begin{bmatrix} 24-190\\ -108+50 \end{bmatrix} =\begin{bmatrix} -166\\ -58 \end{bmatrix}$

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Example Question #161 : Vector & Matrix Quantities

Calculate

$\begin{bmatrix} -10&19 \\ -4& 16 \end{bmatrix} \times \begin{bmatrix} 11\\ 0 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -110\\ 44 \end{bmatrix}$

$\begin{bmatrix} -110\\ -44 \end{bmatrix}$

$\begin{bmatrix} -44\\ -110 \end{bmatrix}$

$\begin{bmatrix} 110\\ 44 \end{bmatrix}$

$\begin{bmatrix} 110\\ -44 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -110\\ -44 \end{bmatrix}$

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.

$\begin{bmatrix} -10&19 \\ -4& 16 \end{bmatrix} \times \begin{bmatrix} 11\\ 0 \end{bmatrix}=\begin{bmatrix} -10\cdot11+19\cdot0\\ -4\cdot 11+16\cdot0 \end{bmatrix} =\begin{bmatrix} -110+0\\ -44+0 \end{bmatrix} =\begin{bmatrix} -110\\ -44 \end{bmatrix}$

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Example Question #161 : Vector & Matrix Quantities

Calculate

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

Possible Answers:

$\begin{bmatrix} 22\\ -48 \end{bmatrix}$

$\begin{bmatrix} -48\\ 22 \end{bmatrix}$

$\begin{bmatrix} 48\\ -22 \end{bmatrix}$

$\begin{bmatrix} -48\\ -22 \end{bmatrix}$

$\begin{bmatrix} 48\\ 22 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 48\\ 22 \end{bmatrix}$

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.

$\begin{bmatrix} -4&6 \\ -9& -8 \end{bmatrix} \times \begin{bmatrix} -6\\ 4 \end{bmatrix}=\begin{bmatrix} (-4)\cdot(-6)+6\cdot4\\ (-9)\cdot (-6)+(-8)\cdot4 \end{bmatrix} =\begin{bmatrix} 24+24\\ 54-32 \end{bmatrix} =\begin{bmatrix} 48\\ 22 \end{bmatrix}$

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

Calculate

$\begin{bmatrix} 8&-11 \\ 9& 20 \end{bmatrix} \times \begin{bmatrix} -8\\ -5 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -172\\ -9 \end{bmatrix}$

$\begin{bmatrix} 9\\ -172 \end{bmatrix}$

$\begin{bmatrix} -9\\ 172 \end{bmatrix}$

$\begin{bmatrix} 9\\ 172 \end{bmatrix}$

$\begin{bmatrix} -9\\ -172 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -9\\ -172 \end{bmatrix}$

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.

$\begin{bmatrix} 8&-11 \\ 9& 20 \end{bmatrix} \times \begin{bmatrix} -8\\ -5 \end{bmatrix}=\begin{bmatrix} 8\cdot(-8)+(-11)\cdot(-5)\\ 9\cdot (-8)+20\cdot(-5) \end{bmatrix} =\begin{bmatrix} -64+55\\ -72-100 \end{bmatrix} =\begin{bmatrix} -9\\ -172 \end{bmatrix}$

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

Calculate

$\begin{bmatrix} -19&-17 \\ 0& -5 \end{bmatrix} \times \begin{bmatrix} 12\\ 19 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -95 \\-551\end{bmatrix}$

$\begin{bmatrix} -551\\ 95 \end{bmatrix}$

$\begin{bmatrix} -551\\ -95 \end{bmatrix}$

$\begin{bmatrix} 551\\ 95 \end{bmatrix}$

$\begin{bmatrix} 551\\ -95 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -551\\ -95 \end{bmatrix}$

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.

$\begin{bmatrix} -19&-17 \\ 0& -5 \end{bmatrix} \times \begin{bmatrix} 12\\ 19 \end{bmatrix}=\begin{bmatrix} -19\cdot12+(-17)\cdot19\\ 0\cdot 12+(-5)\cdot19 \end{bmatrix} =\begin{bmatrix} -228-323\\ 0-95 \end{bmatrix} =\begin{bmatrix} -551\\ -95 \end{bmatrix}$

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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:

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

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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Common Core: High School - Number and Quantity : Vector Multiplication (Matrices being Transformations of Vectors): CCSS.Math.Content.HSN-VM.C.11

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 #151 : Vector & Matrix Quantities

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

Example Question #152 : Vector & Matrix Quantities

Example Question #4 : Vector Multiplication (Matrices Being Transformations Of Vectors): Ccss.Math.Content.Hsn Vm.C.11

Example Question #161 : Vector & Matrix Quantities

Example Question #161 : Vector & Matrix Quantities

Example Question #1 : 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 #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

All Common Core: High School - Number and Quantity Resources

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