Matrix Multiplication Practice Questions

A matrix is a set of numbers arranged in rows and columns to form a rectangular array. Multiplying a matrix by another matrix is called "matrix multiplication."

Matrix Multiplication Practice Questions with Solution

Problem 1: If the matrix A = \begin{pmatrix} 18 \\ 15 \\ -21 \end{pmatrix}

then what is the scalar multiple (-1/3)A?

Solution:

To find (-1/3) A, we have to multiply every element of A by (-1/3). Then

(-1/3) A= 18 x (-1/3) 15 x (-1/3) -21 x (-1/3)

= \begin{pmatrix} -6 & -5 & 7 \end{pmatrix}

Problem 2: Find the product of A and B.

A = \begin{pmatrix} 3 & 2 & -1 \\ 4 & 2 & 0 \end{pmatrix} and B = \begin{pmatrix} 0 & 1 \\ 1 & 2 \\ 3 & 1 \end{pmatrix}

Solution:

Given A = \begin{pmatrix} 3 & 2 & -1 \\ 4 & 2 & 0 \end{pmatrix} and B = \begin{pmatrix} 0 & 1 \\ 1 & 2 \\ 3 & 1 \end{pmatrix}

Product Matrix AB = \begin{pmatrix} 3 \cdot 0 + 2 \cdot 1 + (-1) \cdot 3 & 3 \cdot 1 + 2 \cdot 2 + (-1) \cdot 1 \\ 4 \cdot 0 + 2 \cdot 1 + 0 \cdot 3 & 4 \cdot 1 + 2 \cdot 2 + 0 \cdot 1 \end{pmatrix}

AB = \begin{pmatrix} -1 & 6 \\ 2 & 8 \end{pmatrix}

Problem 3: Find the product of the following matrices:

A = \begin{pmatrix} 1 & 2 & 3 \\ 0 & 2 & 1 \\ 1 & 2 & 5 \end{pmatrix}

B = \begin{pmatrix} 1 & 0 \\ 0 & 1 \\ 2 & 1 \end{pmatrix}

Solution:

Given

A = \begin{pmatrix} 1 & 2 & 3 \\ 0 & 2 & 1 \\ 1 & 2 & 5 \end{pmatrix}

B = \begin{pmatrix} 1 & 0 \\ 0 & 1 \\ 2 & 1 \end{pmatrix}

Then,

A * B = \begin{pmatrix} 1 & 2 & 3 \\ 0 & 2 & 1 \\ 1 & 2 & 5 \end{pmatrix} * \begin{pmatrix} 1 & 0 \\ 0 & 1 \\ 2 & 1 \end{pmatrix}

= \begin{pmatrix} 1 + 0 + 6 & 0 + 2 + 3 \\ 0 + 0 + 2 & 0 + 2 + 1 \\ 1 + 0 + 10 & 0 + 2 + 5 \end{pmatrix}

= \begin{pmatrix} 7 & 5 \\ 2 & 3 \\ 11 & 7 \end{pmatrix}

Practice Questions

1. Given matrices: A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix} and B = \begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix}. Find AB

2. Given matrices: C = \begin{pmatrix} 5 & -1 \\ 2 & 3 \end{pmatrix} and D = \begin{pmatrix} 0 & 4 \\ -2 & 1 \end{pmatrix}. Find CD.

3. Given matrices: E = \begin{pmatrix} 3 & 0 & 2 \\ 1 & 4 & 5 \end{pmatrix} and F = \begin{pmatrix} 2 & 3 \\ 0 & 1 \\ 1 & 4 \end{pmatrix}. Find EF.

4. Given matrices: G = \begin{pmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{pmatrix} and H = \begin{pmatrix} 7 & 8 \\ 9 & 10 \\ 11 & 12 \end{pmatrix}.​​ Find GH.

5. Given matrices: I = \begin{pmatrix} 2 & 4 \\ 6 & 8 \end{pmatrix} and J = \begin{pmatrix} 1 & 3 \\ 5 & 7 \end{pmatrix}. Find IJ.

6. Given matrices: M = \begin{pmatrix} 1 & 0 & 2 \\ -1 & 3 & 1 \end{pmatrix} and N = \begin{pmatrix} 4 & 1 \\ 2 & 2 \\ 0 & 3 \end{pmatrix}. Find MN.