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Common Core: High School - Number and Quantity : Matrices Operations (Add, Subtract, and Multiply): CCSS.Math.Content.HSN-VM.C.8

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Example Questions

Example Question #131 : Vector & Matrix Quantities

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.

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

Apply this to our problem to get,

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

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

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Example Question #132 : Vector & Matrix Quantities

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:

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

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

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

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

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

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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Common Core: High School - Number and Quantity : Matrices Operations (Add, Subtract, and Multiply): CCSS.Math.Content.HSN-VM.C.8

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 #131 : Vector & Matrix Quantities

Example Question #132 : Vector & Matrix Quantities

All Common Core: High School - Number and Quantity Resources

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