Practice Matrix Addition, Subtraction, and Scalar Multiplication in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Matrix addition and subtraction are performed entry by entry on matrices of the same dimensions. Scalar multiplication multiplies every entry of a matrix by a single number (the scalar).
Adding matrices is like adding two spreadsheets cell by cell. If spreadsheet A has sales for January and B has sales for February, then A + B gives total sales in each cell. Scalar multiplication is like giving everyone in the spreadsheet a 10% raise—multiply every entry by 1.1.
Example 1
easyCompute \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} + \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix}.
Example 2
mediumCompute 3 \begin{bmatrix} 2 & -1 \\ 0 & 4 \end{bmatrix} - \begin{bmatrix} 1 & 3 \\ -2 & 5 \end{bmatrix}.
Example 3
easyCompute 2\begin{bmatrix} 4 \\ -3 \end{bmatrix}.
Example 4
mediumIf A = \begin{bmatrix} 1 & 0 \\ -1 & 3 \end{bmatrix} and B = \begin{bmatrix} 2 & 4 \\ 1 & -2 \end{bmatrix}, find A - 2B.