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Given matrices q = [[-7, 5], [2, -3]] and m = [[-1, 4], [7, 8]], find the resulting matrix of 2q - m.

May 13, 2026Mathematics

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Answer

2q - m = \begin{bmatrix} -13 & 6 \\ -3 & -14 \end{bmatrix}

3 steps

Here's how to find $2q - m$ :

Identify the matrices $q$ and $m$ .
$q = \begin{bmatrix} -7 & 5 \\ 2 & -3 \end{bmatrix}$ $m = \begin{bmatrix} -1 & 4 \\ 7 & 8 \end{bmatrix}$
Calculate $2q$ by multiplying each element of matrix $q$ by 2.
$2q = 2 \begin{bmatrix} -7 & 5 \\ 2 & -3 \end{bmatrix} = \begin{bmatrix} 2 \times (-7) & 2 \times 5 \\ 2 \times 2 & 2 \times (-3) \end{bmatrix}$ $2q = \begin{bmatrix} -14 & 10 \\ 4 & -6 \end{bmatrix}$
Subtract matrix $m$ from $2q$ .
$2q - m = \begin{bmatrix} -14 & 10 \\ 4 & -6 \end{bmatrix} - \begin{bmatrix} -1 & 4 \\ 7 & 8 \end{bmatrix}$ $2q - m = \begin{bmatrix} -14 - (-1) & 10 - 4 \\ 4 - 7 & -6 - 8 \end{bmatrix}$ $2q - m = \begin{bmatrix} -14 + 1 & 6 \\ -3 & -14 \end{bmatrix}$ $2q - m = \boxed{\begin{bmatrix} -13 & 6 \\ -3 & -14 \end{bmatrix}}$