Practice Matrix Multiplication in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
To multiply matrices A (m \times n) and B (n \times p), each entry of the result is the dot product of a row from A with a column from B. The number of columns in A must equal the number of rows in B, and the result is an m \times p matrix.
Imagine each row of A as a question and each column of B as an answer key. You 'grade' each row against each column by multiplying corresponding entries and summing. This is why column count of A must match row count of B—the question and answer key must have the same length.
Example 1
mediumCompute \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix}.
Example 2
hardCompute \begin{bmatrix} 2 & 0 & -1 \\ 1 & 3 & 2 \end{bmatrix} \begin{bmatrix} 1 \\ 4 \\ -1 \end{bmatrix}.
Example 3
easyCan you multiply a 2 \times 3 matrix by a 2 \times 3 matrix? Why or why not?
Example 4
mediumCompute \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \begin{bmatrix} 3 & -2 \\ 5 & 7 \end{bmatrix}.