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

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Question

Compute the sum of the two matrices.

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

Answer

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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Question

Compute the sum of the two matrices.

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

Answer

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,

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

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

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Question

Compute the sum of the two matrices.

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

Answer

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,

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

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

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Question

Compute the sum of the two matrices.

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

Answer

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,

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

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

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Question

Compute the sum of the two matrices.

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

Answer

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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Question

Compute the sum of the two matrices.

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

Answer

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,

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

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

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Question

Compute the sum of the two matrices.

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

Answer

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,

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

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

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Question

Compute the sum of the two matrices.

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

Answer

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,

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

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

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Question

Compute the sum of the two matrices.

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

Answer

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,

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

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

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Question

Compute the sum of the two matrices.

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

Answer

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,

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

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

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Question

Compute the sum of the two matrices.

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

Answer

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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Question

Compute the sum of the two matrices.

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

Answer

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,

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

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

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