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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

6 Diagnostic Tests 49 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #115 : Vector & Matrix Quantities

Compute

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

Possible Answers:

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

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

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

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

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

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 #3 : 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 #1 : 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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Example Question #211 : High School: Number And Quantity

Compute

$22\begin{bmatrix} 1 & 1&0 \\ 14&1 &10 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 2 & 22&0 \\ 308&22 &220 \end{bmatrix}$

$\begin{bmatrix} 22 & 22&220 \\ 308&22 &0 \end{bmatrix}$

$\begin{bmatrix} 22 & 22&0 \\ 308&22 &220 \end{bmatrix}$

$\begin{bmatrix} 22 & 22&308 \\ 0&22 &220 \end{bmatrix}$

$\begin{bmatrix} 22 & 0&22 \\ 308&22 &220 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 22 & 22&0 \\ 308&22 &220 \end{bmatrix}$

Explanation:

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

$22\begin{bmatrix} 1 & 1&0 \\ 14&1 &10 \end{bmatrix}=\begin{bmatrix} 22\cdot1 & 22\cdot1&22\cdot0 \\ 22\cdot14&22\cdot1 &22\cdot10 \end{bmatrix}=\begin{bmatrix} 22 & 22&0 \\ 308&22 &220 \end{bmatrix}$

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Example Question #212 : High School: Number And Quantity

Compute

$25\begin{bmatrix} -4 & 18&11 \\ 8&0 &1 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 100 & 450&275\\ 200&0 &25 \end{bmatrix}$

$\begin{bmatrix} -100 & -450&275\\ 200&0 &25 \end{bmatrix}$

$\begin{bmatrix} -100 & 45&27\\ 20&0 &25 \end{bmatrix}$

$\begin{bmatrix} -100 & 450&275\\ 200&0 &25 \end{bmatrix}$

$\begin{bmatrix} -100 & 450&25\\ 200&0 &275 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -100 & 450&275\\ 200&0 &25 \end{bmatrix}$

Explanation:

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

$25\begin{bmatrix} -4 & 18&11 \\ 8&0 &1 \end{bmatrix}=\begin{bmatrix} 25\cdot(-4) & 25\cdot18&25\cdot11 \\ 25\cdot8&25\cdot0 &-25\cdot1 \end{bmatrix}=\begin{bmatrix} -100 & 450&275\\ 200&0 &25 \end{bmatrix}$

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Example Question #213 : High School: Number And Quantity

Compute the sum of the two matrices.

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

Possible Answers:

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

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

Not possible

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

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

Correct answer:

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

Explanation:

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

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

Apply this to our problem to get,

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

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

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Example Question #214 : High School: Number And Quantity

Compute the sum of the two matrices.

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

Apply this to our problem to get,

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

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

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Example Question #215 : High School: Number And Quantity

Compute the sum of the two matrices.

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

Apply this to our problem to get,

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

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

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Example Question #216 : High School: Number And Quantity

Compute the sum of the two matrices.

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

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

Apply this to our problem to get,

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

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

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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 #115 : Vector & Matrix Quantities

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

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 #211 : High School: Number And Quantity

Example Question #212 : High School: Number And Quantity

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

All Common Core: High School - Number and Quantity Resources

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