How to add matrices - ACT Math

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Question

Simplify:

$\begin{bmatrix} 14&22\ -3 &4 \end{bmatrix}+\begin{bmatrix} -3&12\ 5 &-10 \end{bmatrix}$

Answer

Matrix addition is very easy! All that you need to do is add each correlative member to each other. Think of it like this:

$\begin{bmatrix} 14&22\ -3 &4 \end{bmatrix}+\begin{bmatrix} -3&12\ 5 &-10 \end{bmatrix}=\begin{bmatrix} 14-3&22+12\ -3+5 &4-10 \end{bmatrix}$

Now, just simplify:

$\begin{bmatrix} 11&34\ 2 &-6 \end{bmatrix}$

There is your answer!

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Question

Simplify:

$\begin{bmatrix} -5&7\ 102 & -12 \end{bmatrix}+\begin{bmatrix} 3&107\ -10 & -9 \end{bmatrix}$

Answer

Matrix addition is really easy—don't overthink it! All you need to do is combine the two matrices in a one-to-one manner for each index:

$\begin{bmatrix} -5&7\ 102 & -12 \end{bmatrix}+\begin{bmatrix} 3&107\ -10 & -9 \end{bmatrix}=\begin{bmatrix} -5+3&7+107\ 102-10 & -12-9 \end{bmatrix}$

Then, just simplify all of those simple additions and subtractions:

$\begin{bmatrix} -5+3&7+107\ 102-10 & -12-9 \end{bmatrix}=\begin{bmatrix} -2&114\ 92 & -21 \end{bmatrix}$

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Question

What is the value of

$\begin{bmatrix}2 & 2\ 3& -1 \end{bmatrix}$ $+\begin{bmatrix}0 &1 \ -1& 12 \end{bmatrix}$ ?

Answer

To add matrices you simply add the numbers in the same position as each other.

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

Plugging the given values into the above formula, we are able to solve the question.

$\begin{bmatrix}2 & 2\ 3& -1 \end{bmatrix}$ $+\begin{bmatrix}0 &1 \ -1& 12 \end{bmatrix}$ $=\begin{bmatrix} 2+0&2+1 \ 3+(-1)&-1+12 \end{bmatrix}$

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