Skill: Subtract matrices

To subtract matrices, first check that they have the same number of rows and columns. Then subtract each entry of the second matrix from the entry in the matching position of the first. The result has the same dimensions as the original matrices.

For example, calculate

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

Both matrices are $2 \times 3$, so subtraction is defined. Subtract corresponding entries:

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

Remember: subtract in the same order as the matrices are written.