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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 #1 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Compute the sum of the two matrices.

$\begin{bmatrix} 4 & 1 & 0\\ 5& 1&3 \end{bmatrix} + \begin{bmatrix} 5&0 &2 \\ 3&-2 & 5 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} -9&1 &2 \\ 8& -1& 8 \end{bmatrix}$

$\begin{bmatrix} 9&-1 &-2 \\ 8& -1& 8 \end{bmatrix}$

$\begin{bmatrix} 9&1 &2 \\ 8& 1& 8 \end{bmatrix}$

$\begin{bmatrix} 9&1 &8 \\ 8& -1& 2 \end{bmatrix}$

$\begin{bmatrix} 9&1 &2 \\ 8& -1& 8 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 9&1 &2 \\ 8& -1& 8 \end{bmatrix}$

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,

$\begin{bmatrix} 4 & 1 & 0\\ 5& 1&3 \end{bmatrix} + \begin{bmatrix} 5&0 &2 \\ 3&-2 & 5 \end{bmatrix}=\begin{bmatrix} 4+5& 1+0 & 0+2 \\ 5+3& 1+(-2) & 3+5 \end{bmatrix}$

$=\begin{bmatrix} 9&1 &2 \\ 8& -1& 8 \end{bmatrix}$

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Example Question #124 : Vector & Matrix Quantities

Compute the sum of the two matrices.

$\begin{bmatrix} -2 & -4 & 6\\-4& -4& -5 \end{bmatrix} + \begin{bmatrix} 3&-1 &-4 \\ 7&6 & -4 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 1&5 &2 \\ 3& 2& -9 \end{bmatrix}$

$\begin{bmatrix} 1&5 &2 \\ 3& 2& 9 \end{bmatrix}$

$\begin{bmatrix} 1&-5 &2 \\ 3& 2& -9 \end{bmatrix}$

$\begin{bmatrix} 1&-5 &-2 \\ -3& 2& -9 \end{bmatrix}$

$\begin{bmatrix} 1&-5 &2 \\ 3& 2& 9 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 1&-5 &2 \\ 3& 2& -9 \end{bmatrix}$

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,

$\begin{bmatrix} -2 & -4 & 6\\-4& -4& -5 \end{bmatrix} + \begin{bmatrix} 3&-1 &-4 \\ 7&6 & -4 \end{bmatrix}=\begin{bmatrix} (-2)+3& (-4)+(-1) & 6+(-4) \\ (-4)+7& (-4)+6 & (-5)+(-4) \end{bmatrix}$

$=\begin{bmatrix} 1&-5 &2 \\ 3& 2& -9 \end{bmatrix}$

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Example Question #5 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Compute the sum of the two matrices.

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

Possible Answers:

$\begin{bmatrix} 4&8 &0 \\ 9& 0& 6 \end{bmatrix}$

$\begin{bmatrix} 4&-8 &0 \\ 9& 6& 0 \end{bmatrix}$

$\begin{bmatrix} 4&-8 &0 \\ 9& 0& 6 \end{bmatrix}$

$\begin{bmatrix} 4&-8 &0 \\ 0& 9& 6 \end{bmatrix}$

$\begin{bmatrix} 4&0 &0 \\ 9& -8& 6 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 4&-8 &0 \\ 9& 0& 6 \end{bmatrix}$

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.

Apply this to our problem to get,

$\begin{bmatrix} 1 & -4 & 3\\ 4& 1& 4 \end{bmatrix} + \begin{bmatrix} 3&-4 &-3 \\ 5&-1 & 2 \end{bmatrix}=\begin{bmatrix} 1+3& (-4)+(-4) & 3+(-3) \\ 4+5& 1+(-1) & 4+2 \end{bmatrix}$

$=\begin{bmatrix} 4&-8 &0 \\ 9& 0& 6 \end{bmatrix}$

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Example Question #1 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Compute the sum of the two matrices.

$\begin{bmatrix} 0 & -3 & -3\\ -4& -3& -2 \end{bmatrix} + \begin{bmatrix} 4&-5 &-1 \\ -1&-5 & 0 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 4&8 &-4 \\ -5& 8& -2 \end{bmatrix}$

$\begin{bmatrix} 4&-8 &-2 \\ -5& -8& -4 \end{bmatrix}$

$\begin{bmatrix} 4&8 &-4 \\ -5& -8& -2 \end{bmatrix}$

$\begin{bmatrix} 4&-8 &-4 \\ -5& -8& -2 \end{bmatrix}$

$\begin{bmatrix} 4&8 &4 \\ 5& 8& 2 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 4&-8 &-4 \\ -5& -8& -2 \end{bmatrix}$

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,

$\begin{bmatrix} 0 & -3 & -3\\ -4& -3& -2 \end{bmatrix} + \begin{bmatrix} 4&-5 &-1 \\ -1&-5 & 0 \end{bmatrix}=\begin{bmatrix} 0+4& -3+(-5) & (-3)+(-1) \\ (-4)+(-1)& (-3)+(-5) & (-2)+0 \end{bmatrix}$

$=\begin{bmatrix} 4&-8 &-4 \\ -5& -8& -2 \end{bmatrix}$

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Example Question #7 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Compute the sum of the two matrices.

$\begin{bmatrix} 5 & 0 & -5\\ -5& 3& -1 \end{bmatrix} + \begin{bmatrix} 6&-2 &-5 \\ -5&5 & -4 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 11&2 &-10 \\ -10& 8& -5 \end{bmatrix}$

$\begin{bmatrix} 11&-2 &10 \\ 10& 8& -5 \end{bmatrix}$

$\begin{bmatrix} -11&-2 &-10 \\ -10& 8& -5 \end{bmatrix}$

$\begin{bmatrix} 11&-2 &10 \\ -10& 8& 5 \end{bmatrix}$

$\begin{bmatrix} 11&-2 &-10 \\ -10& 8& -5 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 11&-2 &-10 \\ -10& 8& -5 \end{bmatrix}$

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,

$\begin{bmatrix} 5 & 0 & -5\\ -5& 3& -1 \end{bmatrix} + \begin{bmatrix} 6&-2 &-5 \\ -5&5 & -4 \end{bmatrix}=\begin{bmatrix} 5+6& 0+(-2) & (-5)+(-5) \\ (-5)+(-5)& 3+5 & (-1)+(-4) \end{bmatrix}$

$=\begin{bmatrix} 11&-2 &-10 \\ -10& 8& -5 \end{bmatrix}$

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Example Question #3 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Compute the sum of the two matrices.

$\begin{bmatrix} 3 & -2 & 5\\ -3& -5& 5 \end{bmatrix} + \begin{bmatrix} 7&0 &0 \\ -4&2 & -2 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 10&-2 &5 \\ 7& -3& 3 \end{bmatrix}$

$\begin{bmatrix} 10&-2 &3 \\ -7& -3& 5 \end{bmatrix}$

$\begin{bmatrix} 10&-2 &5 \\ -7& 3& 3 \end{bmatrix}$

$\begin{bmatrix} 10&-2 &5 \\ -7& -3& 3 \end{bmatrix}$

$\begin{bmatrix} 10&2 &5 \\ 7& 3& 3 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 10&-2 &5 \\ -7& -3& 3 \end{bmatrix}$

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,

$\begin{bmatrix} 3 & -2 & 5\\ -3& -5& 5 \end{bmatrix} + \begin{bmatrix} 7&0 &0 \\ -4&2 & -2 \end{bmatrix}=\begin{bmatrix} 3+7& (-2)+0 & 5+0 \\ (-3)+(-4)& (-5)+2 & 5+(-2) \end{bmatrix}$

$=\begin{bmatrix} 10&-2 &5 \\ -7& -3& 3 \end{bmatrix}$

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Example Question #11 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Compute the sum of the two matrices.

$\begin{bmatrix} -1 & 5 & -4\\ -1& -1& -3 \end{bmatrix} + \begin{bmatrix} 2&3 &6 \\ -4&-5 & -1 \end{bmatrix}$

Possible Answers:

$\begin{bmatrix} 1&8 &2 \\ -5& -6& -4 \end{bmatrix}$

$\begin{bmatrix} 1&8 &2 \\ -5& 6& -4 \end{bmatrix}$

$\begin{bmatrix} 1&8 &2 \\ 5& 6& 4 \end{bmatrix}$

$\begin{bmatrix} 1&8 &2 \\ -5& 6& 4 \end{bmatrix}$

$\begin{bmatrix} 1&8 &2 \\ 5& -6& -4 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 1&8 &2 \\ -5& -6& -4 \end{bmatrix}$

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,

$\begin{bmatrix} -1 & 5 & -4\\ -1& -1& -3 \end{bmatrix} + \begin{bmatrix} 2&3 &6 \\ -4&-5 & -1 \end{bmatrix}=\begin{bmatrix} (-1)+2& 5+3 & (-4)+6 \\ (-1)+(-4)& (-1)+(-5) & (-3)+(-1) \end{bmatrix}$

$=\begin{bmatrix} 1&8 &2 \\ -5& -6& -4 \end{bmatrix}$

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Example Question #12 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Compute the sum of the two matrices.

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

Possible Answers:

$\begin{bmatrix} -6&2 &-2 \\ 6& -3& 5 \end{bmatrix}$

$\begin{bmatrix} 0&2 &-2 \\ 6& -3& 5 \end{bmatrix}$

$\begin{bmatrix} -6&2 &-2 \\ 6& 3& 5 \end{bmatrix}$

$\begin{bmatrix} 6&2 &2 \\ 6& 3& 5 \end{bmatrix}\,$

$\begin{bmatrix} -6&2 &2 \\ 6& -3& 5 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -6&2 &-2 \\ 6& -3& 5 \end{bmatrix}$

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,

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

$=\begin{bmatrix} -6&2 &-2 \\ 6& -3& 5 \end{bmatrix}$

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Example Question #221 : High School: Number And Quantity

Which of the following properties does not apply to matrices?

Possible Answers:

Associative

None of the answers

Distributive

Commutative

Correct answer:

Commutative

Explanation:

Commutative does not apply to matrices because if we have matrices , and . It is not necessarily true that $A\times B=B\times A$ , even though in some cases it's true.

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Example Question #222 : High School: Number And Quantity

Which is an example of two matrices satisfying the associative and distributive properties? Let a be a scalar, and A, B, and C be three unique matrices.

Possible Answers:

a(A+B)=aA+aB

A+(B+C)=(A+B)+C

$A\times B=B\times A$

a(A+B)+C=aA+(aB+C)

Correct answer:

a(A+B)+C=aA+(aB+C)

Explanation:

a(A+B)+C=aA+(aB+C) is the correct answer because it is the only answer that involves both the associative and distributive properties.

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All Common Core: High School - Number and Quantity Resources

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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 #1 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Example Question #124 : Vector & Matrix Quantities

Example Question #5 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Example Question #1 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Example Question #7 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Example Question #3 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Example Question #11 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Example Question #12 : Matrices Operations (Add, Subtract, And Multiply): Ccss.Math.Content.Hsn Vm.C.8

Example Question #221 : High School: Number And Quantity

Example Question #222 : High School: Number And Quantity

All Common Core: High School - Number and Quantity Resources

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