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Common Core: High School - Number and Quantity : Multiply Matrices by Scalar: CCSS.Math.Content.HSN-VM.C.7

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

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Example Questions

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:

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

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

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

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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Example Question #3 : Multiply Matrices By Scalar: Ccss.Math.Content.Hsn Vm.C.7

Compute

$-17\begin{bmatrix} -9 & -12&16\\ 0&-7 &10 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 153 & -204&-272 \\ 0&119 &-170 \end{bmatrix}$

$\begin{bmatrix} 153 & 204&-272 \\ 0&119 &170 \end{bmatrix}$

$\begin{bmatrix} 153 & 204&-272 \\ 0&119 &-170 \end{bmatrix}$

$\begin{bmatrix} 153 & 204&272 \\ 0&119 &-170 \end{bmatrix}$

$\begin{bmatrix} 153 & 204&272 \\ 0&119 &170 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 153 & 204&-272 \\ 0&119 &-170 \end{bmatrix}$

Explanation:

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

$-17\begin{bmatrix} -9 & -12&16\\ 0&-7 &10 \end{bmatrix}=\begin{bmatrix} -17\cdot(-9) & -17\cdot(-12)&-17\cdot16 \\ -17\cdot0&-17\cdot-7 &-17\cdot10 \end{bmatrix}=\begin{bmatrix} 153 & 204&-272 \\ 0&119 &-170 \end{bmatrix}$

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Example Question #4 : Multiply Matrices By Scalar: Ccss.Math.Content.Hsn Vm.C.7

Compute

$-19\begin{bmatrix} 4 & 0&17 \\ 7&15 &-9 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -76& 0&-323 \\ -133&-285 &-171 \end{bmatrix}$

$\begin{bmatrix} 76& 0&-323 \\ -133&285 &171 \end{bmatrix}$

$\begin{bmatrix} -76& 0&-323 \\ -133&-285 &171 \end{bmatrix}$

$\begin{bmatrix} -76& 0&-223 \\ -133&-285 &171 \end{bmatrix}$

$\begin{bmatrix} -76& 0&323 \\ 133&-285 &171 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -76& 0&-323 \\ -133&-285 &171 \end{bmatrix}$

Explanation:

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

$-19\begin{bmatrix} 4 & 0&17 \\ 7&15 &-9 \end{bmatrix}=\begin{bmatrix} -19\cdot4 & -19\cdot0&-19\cdot17 \\ -19\cdot7&-19\cdot15 &-19\cdot(-9) \end{bmatrix}=\begin{bmatrix} -76& 0&-323 \\ -133&-285 &171 \end{bmatrix}$

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

Compute

$21\begin{bmatrix} 9 & 3-&2 \\ 14&0 &14 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -189 & -63&-42 \\ 294&0 &-294 \end{bmatrix}$

$\begin{bmatrix} 189 & -63&42 \\ -294&0 &294 \end{bmatrix}$

$\begin{bmatrix} 189 & -63&42 \\ 94&0 &94 \end{bmatrix}$

$\begin{bmatrix} 189 & -63&42 \\ -294&0 &-294 \end{bmatrix}$

$\begin{bmatrix} 189 & -63&42 \\ 294&0 &294 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 189 & -63&42 \\ 294&0 &294 \end{bmatrix}$

Explanation:

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

$21\begin{bmatrix} 9 & -3&2 \\ 14&0 &14 \end{bmatrix}=\begin{bmatrix} 21\cdot9 & 21\cdot(-3)&21\cdot2 \\ 21\cdot14&21\cdot0 &21\cdot14 \end{bmatrix}=\begin{bmatrix} 189 & -63&42 \\ 294&0 &294 \end{bmatrix}$

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Example Question #6 : Multiply Matrices By Scalar: Ccss.Math.Content.Hsn Vm.C.7

Compute

$7\begin{bmatrix} 7 & 12&-3 \\ 17&3 &6 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 49 & 84&-21 \\ 119&21 &42 \end{bmatrix}$

$\begin{bmatrix} -49 & 84&-21 \\ 119&21 &-42 \end{bmatrix}$

$\begin{bmatrix} 9 & 84&-21 \\ 19&21 &2 \end{bmatrix}$

$\begin{bmatrix} 49 & 4&-21 \\ 119&1 &42 \end{bmatrix}$

$\begin{bmatrix} -49 & -84&-21 \\ -119&-21 &-42 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 49 & 84&-21 \\ 119&21 &42 \end{bmatrix}$

Explanation:

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

$7\begin{bmatrix} 7 & 12&-3 \\ 17&3 &6 \end{bmatrix}=\begin{bmatrix} 7\cdot7 & 7\cdot12&7\cdot(-3) \\ 7\cdot17&7\cdot3 &7\cdot6 \end{bmatrix}=\begin{bmatrix} 49 & 84&-21 \\ 119&21 &42 \end{bmatrix}$

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

Compute

$22\begin{bmatrix} 7 & 6&16 \\ 0&0 &12 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 154 & 132&352 \\ 0&0 & 264\end{bmatrix}$

$\begin{bmatrix} 154 & 0&352 \\ 0&132 &264 \end{bmatrix}$

$\begin{bmatrix} 154 & 0&352 \\ 0&132 & 264\end{bmatrix}$

$\begin{bmatrix} 154 & 132&-352 \\ 0&0 & -264\end{bmatrix}$

$\begin{bmatrix} 154 & 132&352 \\ 0&0 &264 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 154 & 132&352 \\ 0&0 &264 \end{bmatrix}$

Explanation:

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

$22\begin{bmatrix} 7 & 6&16 \\ 0&0 &12 \end{bmatrix}=\begin{bmatrix} 22\cdot7 & 22\cdot6&22\cdot16 \\ 22\cdot0&22\cdot0 &22\cdot12 \end{bmatrix}=\begin{bmatrix} 154 & 132&352 \\ 0&0 &264 \end{bmatrix}$

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

Compute

$-4\begin{bmatrix} 5 & 2&12 \\ 3&-1 &-2 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 20 & -8&-48 \\ -12&4 &8 \end{bmatrix}$

$\begin{bmatrix} -20 & -8&48 \\ 12&4 &8 \end{bmatrix}$

$\begin{bmatrix} -20 & 8&48 \\ -12&4 &8 \end{bmatrix}$

$\begin{bmatrix} -20 & -8&-48 \\ -12&4 &8 \end{bmatrix}$

$\begin{bmatrix} 20 & 8&48 \\ 12&4 &8 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -20 & -8&-48 \\ -12&4 &8 \end{bmatrix}$

Explanation:

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

$-4\begin{bmatrix} 5 & 2&12 \\ 3&-1 &-2 \end{bmatrix}=\begin{bmatrix} -4\cdot5 & -4\cdot2&-4\cdot12 \\ -4\cdot3&-4\cdot(-1) &-4\cdot(-2) \end{bmatrix}=\begin{bmatrix} -20 & -8&-48 \\ -12&4 &8 \end{bmatrix}$

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

Compute

$4\begin{bmatrix} 10 & -4&5 \\ 6&-1 &1 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -40 & -16&-20 \\ 24&-4 &4 \end{bmatrix}$

$\begin{bmatrix} 40 & 16&20 \\ 24&4 &4 \end{bmatrix}$

$\begin{bmatrix} 40 & -16&20 \\ 24&4 &4 \end{bmatrix}$

$\begin{bmatrix} 40 & -16&20 \\ 24&-4 &4 \end{bmatrix}$

$\begin{bmatrix} -40 & -16&-20 \\ -24&-4 &-4 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 40 & -16&20 \\ 24&-4 &4 \end{bmatrix}$

Explanation:

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

$4\begin{bmatrix} 10 & -4&5 \\ 6&-1 &1 \end{bmatrix}=\begin{bmatrix} 4\cdot10 & 4\cdot(-4)&4\cdot5 \\ 4\cdot6&4\cdot(-1) &4\cdot1 \end{bmatrix}=\begin{bmatrix} 40 & -16&20 \\ 24&-4 &4 \end{bmatrix}$

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

Compute

$14\begin{bmatrix} 17 & -2&3 \\ -5&-1 &2 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 238 & -28&42 \\ -70&-14 &28 \end{bmatrix}$

$\begin{bmatrix} 238 & 28&42 \\ 70&14 &28 \end{bmatrix}$

$\begin{bmatrix} 238 & 28&42 \\ -70&-14 &28 \end{bmatrix}$

$\begin{bmatrix} 238 & -28&42 \\ 70&-14 &28 \end{bmatrix}$

$\begin{bmatrix} 238 & 28&42 \\ 70&-14 &28 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 238 & -28&42 \\ -70&-14 &28 \end{bmatrix}$

Explanation:

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

$14\begin{bmatrix} 17 & -2&3 \\ -5&-1 &2 \end{bmatrix}=\begin{bmatrix} 14\cdot17 & 14\cdot(-2)&14\cdot3 \\ 14\cdot(-5)&14\cdot(-1) &14\cdot2 \end{bmatrix}=\begin{bmatrix} 238 & -28&42 \\ -70&-14 &28 \end{bmatrix}$

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Common Core: High School - Number and Quantity : Multiply Matrices by Scalar: CCSS.Math.Content.HSN-VM.C.7

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 #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

Example Question #3 : Multiply Matrices By Scalar: Ccss.Math.Content.Hsn Vm.C.7

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

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

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All Common Core: High School - Number and Quantity Resources

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