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ACT Math : How to subtract matrices

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Example Question #1 : Find The Difference Of Two Matrices

Given the following matrices, what is the product of and ?

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

Possible Answers:

Correct answer:

Explanation:

When subtracting matrices, you want to subtract each corresponding cell.

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

Now solve for and

x-1=4

x=5

1-y=-8

y=9

xy = 45

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Example Question #1 : Find The Difference Of Two Matrices

If $\begin{bmatrix} a&b\\ c&d \end{bmatrix} + \begin{bmatrix} 3&14\\ 12&4 \end{bmatrix} = \begin{bmatrix} 19&2\\ 4&5 \end{bmatrix}$ , what is a+b+c+d ?

Possible Answers:

Correct answer:

Explanation:

You can treat matrices just like you treat other members of an equation. Therefore, you can subtract the matrix

$\begin{bmatrix} 3&14\\ 12&4 \end{bmatrix}$

from both sides of the equation. This gives you:

$\begin{bmatrix} a&b\\ c&d \end{bmatrix}=\begin{bmatrix} 19&2\\ 4&5 \end{bmatrix}-\begin{bmatrix} 3&14\\ 12&4 \end{bmatrix}$

Now, matrix subtraction is simple. You merely subtract each element, matching the correlative spaces with each other:

$\begin{bmatrix} a&b\\ c&d \end{bmatrix} = \begin{bmatrix} 19-3&2-14\\ 4-12&5-4 \end{bmatrix}$

Then, you simplify:

$\begin{bmatrix} 19-3&2-14\\ 4-12&5-4 \end{bmatrix} = \begin{bmatrix} 16&-12\\ -8&1 \end{bmatrix}$

Therefore, a+b+c+d = 16-12-8+1=-3

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Example Question #1 : How To Subtract Matrices

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

Possible Answers:

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

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

$\begin{bmatrix} -4&6 \\ 1&-1 \end{bmatrix}$

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

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

Correct answer:

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

Explanation:

When subtracting matrices, subtracting component-wise.

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

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

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

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Example Question #2 : How To Subtract Matrices

If $\begin{bmatrix} 12& 14\\ -4 & -2 \\ 3 & 3 \end{bmatrix}- \begin{bmatrix} 9& -1\\ 4 & -5 \\ 6 & -9 \end{bmatrix}=\begin{bmatrix} a&b\\c&d\\e&f\end{bmatrix}$ , then what is the value of a+f ?

Possible Answers:

Correct answer:

Explanation:

Match each term from the first matrix with the corresponding number from the second matrix and subtract.

$\begin{bmatrix} 12 -9 & 14 - (-1) \\ -4 -4 & -2-(-5) \\ 3-6 & 3-(-9) \end{bmatrix}$

Simplify.

$\begin{bmatrix} 12 -9 & 14 - (-1) \\ -4 -4 & -2-(-5) \\ 3-6 & 3-(-9) \end{bmatrix} = \begin{bmatrix} 3& 15 \\ -8 & 3 \\ -3 & 12 \end{bmatrix}$

Each of the numbers in the matrix solution now corresponds to the letters, a through f. Add a (upper left) and f (lower right).

a+f=3+12=15

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ACT Math : How to subtract matrices

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Find The Difference Of Two Matrices

Example Question #1 : Find The Difference Of Two Matrices

Example Question #1 : How To Subtract Matrices

Example Question #2 : How To Subtract Matrices

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