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Flashcards: Matrices Operations (Add, Subtract, and Multiply): CCSS.Math.Content.HSN-VM.C.8

Compute the sum of the two matrices.

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

Not possible

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

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

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

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

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Flashcards: Matrices Operations (Add, Subtract, and Multiply): CCSS.Math.Content.HSN-VM.C.8

Compute the sum of the two matrices.

Not possible

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

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

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

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

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Flashcards: Matrices Operations (Add, Subtract, and Multiply): CCSS.Math.Content.HSN-VM.C.8

Compute the sum of the two matrices.

Your answer:

Not possible

Your answer:

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

Your answer:

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

Your answer:

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

Correct answer:

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

Explanation:

In order to compute the sum of the two matrices, we need to sum up identical entries. This means we sum up $\displaystyle 4$ , and $\displaystyle 2$ , then $\displaystyle 10$ , and $\displaystyle -8$ , and etc. The computation in general looks like the following.

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

Apply this to our problem to get,

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

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

Flashcards: Matrices Operations (Add, Subtract, and Multiply): CCSS.Math.Content.HSN-VM.C.8

Compute the sum of the two matrices.

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

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

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

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

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

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

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Flashcards: Matrices Operations (Add, Subtract, and Multiply): CCSS.Math.Content.HSN-VM.C.8

Compute the sum of the two matrices.

Your answer:

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

Your answer:

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

Your answer:

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

Your answer:

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

Correct answer:

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

Explanation:

In order to compute the sum of the two matrices, we need to sum up identical entries. This means we sum up $\displaystyle -2$ , and $\displaystyle 2$ , then $\displaystyle -3$ , and $\displaystyle 2$ , and etc. The computation in general looks like the following.

Apply this to our problem to get,

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

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

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Flashcards: Matrices Operations (Add, Subtract, and Multiply): CCSS.Math.Content.HSN-VM.C.8

All Common Core: High School - Number and Quantity Resources

Flashcards: Matrices Operations (Add, Subtract, and Multiply): CCSS.Math.Content.HSN-VM.C.8

Flashcards: Matrices Operations (Add, Subtract, and Multiply): CCSS.Math.Content.HSN-VM.C.8

Flashcards: Matrices Operations (Add, Subtract, and Multiply): CCSS.Math.Content.HSN-VM.C.8

Flashcards: Matrices Operations (Add, Subtract, and Multiply): CCSS.Math.Content.HSN-VM.C.8

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