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ACT Math : How to add matrices

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Example Questions

Example Question #3 : Matrices

Simplify:

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

Possible Answers:

$\begin{bmatrix} 17&10\\ -8 &14 \end{bmatrix}$

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

$\begin{bmatrix} 45&-4 \end{bmatrix}$

$\begin{bmatrix} 17 & -5 \\ 3 & 1 \end{bmatrix}$

$\begin{bmatrix} 13\\ 28 \end{bmatrix}$

Correct answer:

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

Explanation:

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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Example Question #4 : Matrices

Simplify:

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

Possible Answers:

$\begin{bmatrix} 90\\ 93 \end{bmatrix}$

$\begin{bmatrix} 112\\ 71 \end{bmatrix}$

$\begin{bmatrix} -8&-100\\ 112 & -3 \end{bmatrix}$

$\begin{bmatrix} 112 & 71\end{bmatrix}$

$\begin{bmatrix} -2&114\\ 92 & -21 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} -2&114\\ 92 & -21 \end{bmatrix}$

Explanation:

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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Example Question #21 : Matrices

What is the value of

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

Possible Answers:

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

$\begin{bmatrix} 2&1 \\ 4&11 \end{bmatrix}$

$\begin{bmatrix} 2&3 \\ 2&11 \end{bmatrix}$

You cannot add these two matrices because their indices do not line up.

$\begin{bmatrix} 20&21 \\ -31&-121 \end{bmatrix}$

Correct answer:

$\begin{bmatrix} 2&3 \\ 2&11 \end{bmatrix}$

Explanation:

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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ACT Math : How to add matrices

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #3 : Matrices

Example Question #4 : Matrices

Example Question #21 : Matrices

All ACT Math Resources

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