How to Multiply Matrix? (+FREE Worksheet!)
Here is a step-by-step guide to multiply matrices. The exercises can help you measure your knowledge of matrix multiplication.
Related Topics
Step by step guide to multiply matrices
- Step 1: Make sure that it’s possible to multiply the two matrices (the number of columns in the 1st one should be the same as the number of rows in the second one.)
- Step 2: The elements of each row of the first matrix should be multiplied by the elements of each column in the second matrix.
- Step 3: Add the products.
Matrix Multiplication – Example 1:
\(\begin{bmatrix}-5 & -5 \\-1 & 2 \end{bmatrix}\)\(\begin{bmatrix}-2 & -3 \\3 & 5 \end{bmatrix}\)
Solution:
Multiply the rows of the first matrix by the columns of the second matrix. \(\begin{bmatrix}(-5)(-2)+(-5)(3) & (-5)(-3)+(-5)(5) \\(-1)(-2)+(2)(3) & (-1)(-3)+(2)(5) \end{bmatrix}= \begin{bmatrix}(10)+(-15) & (15)+(-25) \\(2)+(6) & (3)+(10) \end{bmatrix}=\begin{bmatrix}-5 & -10 \\8 & 13 \end{bmatrix}\)
The Absolute Best Books to Ace Pre-Algebra to Algebra II
Matrix Multiplication – Example 2:
\(\begin{bmatrix}-4 & -6&-6 \\0 & 6&3 \end{bmatrix}\begin{bmatrix}0 \\-3 \\0 \end{bmatrix}\)
Solution:
Multiply the rows of the first matrix by the columns of the second matrix. \(\begin{bmatrix}(-4)(0)+(-6)(-3)+(-6)(0) \\(0)(0)+(6)(-3)+(3)(0) \end{bmatrix}=\begin{bmatrix}0+18+0 \\0-18+0 \end{bmatrix}=\begin{bmatrix}18 \\-18 \end{bmatrix}\)
Matrix Multiplication – Example 3:
\(\begin{bmatrix}1 & 3 \\2 & 4 \end{bmatrix}\)\(\begin{bmatrix}2 &4 \\-2 & 1 \end{bmatrix}\)
Solution:
\(\begin{bmatrix}(1) (2)+(3)(-2) & (1) (4)+(3) (1) \\(2) (2)+ (4)(-2) & (2) (4)+(4) (1) \end{bmatrix}=\begin{bmatrix}(2)+(-6) & (4)+(3) \\(4)+ (-8) & (8)+(4) \end{bmatrix}=\begin{bmatrix}-4 & 7 \\-4 & 12 \end{bmatrix}\)
The Best Book to Help You Ace Pre-Algebra
Matrix Multiplication – Example 4:
\(\begin{bmatrix}2 & -1&-1 \\3 & 1&5 \end{bmatrix}\begin{bmatrix}-2 \\-1 \\4 \end{bmatrix}\)
Solution:
Multiply the rows of the first matrix by the columns of the second matrix. \(\begin{bmatrix}(2)(-2)+(-1)(-1)+(-1) (4)\\(3)(-2)+(1)(-1)+(5) (4) \end{bmatrix}=\begin{bmatrix}(-4)+(1)+(-4)\\(-6)+(-1)+(20) \end{bmatrix}=\begin{bmatrix}-7 \\13 \end{bmatrix}\)
Exercises for Multiplying Matrix
Solve.
- \(\color{blue}{\begin{bmatrix}0 & 2 \\-2 & -5 \end{bmatrix}\begin{bmatrix}6 & -6 \\3 & 0 \end{bmatrix}}\)
- \(\color{blue}{\begin{bmatrix}3 & -1 \\-3 & 6\\-6&-6 \end{bmatrix}\begin{bmatrix}-1 & 6 \\5 & 4\end{bmatrix}}\)
- \(\color{blue}{\begin{bmatrix}0 & 5 \\-3 & 1\\-5&1 \end{bmatrix}\begin{bmatrix}-4 & 4 \\-2 & -4\end{bmatrix}}\)
- \(\color{blue}{\begin{bmatrix}5 & 3&5 \\1 & 5&0 \end{bmatrix}\begin{bmatrix}-4 & 2 \\-3 & 4\\3&-5 \end{bmatrix}}\)
- \(\color{blue}{\begin{bmatrix}4 & 5 \\-4 & 6\\-5&-6 \end{bmatrix}\begin{bmatrix}4 & 6 \\6& 2\\-4&1 \end{bmatrix}}\)
- \(\color{blue}{\begin{bmatrix}-2 & -6 \\-4 & 3\\5&0 \\4&-6\end{bmatrix}\begin{bmatrix}2 & -2&2 \\-2 &0&-3 \end{bmatrix}}\)
- \(\color{blue}{\begin{bmatrix}6 & 0 \\-27 & 12 \end{bmatrix}}\)
- \(\color{blue}{\begin{bmatrix}-8 & 14 \\33 & 6\\ -24&-60\end{bmatrix}}\)
- \(\color{blue}{\begin{bmatrix}-10 & -20 \\10 & -16\\ 18&-24\end{bmatrix}}\)
- \(\color{blue}{\begin{bmatrix}-14 & -3 \\-19 & 22 \end{bmatrix}}\)
- \(\color{blue}{Undefined}\)
- \(\color{blue}{\begin{bmatrix}8 & 4&14\\-14 & 8&-17\\10&-10&10 \\20&-8&26\end{bmatrix}}\)
The Greatest Books for Students to Ace the Algebra
Related to This Article
More math articles
- 10 Most Common 8th Grade MCAS Math Questions
- Top 10 4th Grade STAAR Math Practice Questions
- How to Divide Mixed Numbers? (+FREE Worksheet!)
- 10 Most Common 6th Grade SBAC Math Questions
- 3rd Grade ACT Aspire Math Worksheets: FREE & Printable
- How to Find Mean, Median, Mode, and Range of the Given Data? (+FREE Worksheet!)
- 6th Grade ACT Aspire Math Worksheets: FREE & Printable
- 10 Most Common 5th Grade OST Math Questions
- 6th Grade SOL Math Worksheets: FREE & Printable
- How to Find the y-Intercept of a Line?
What people say about "How to Multiply Matrix? (+FREE Worksheet!) - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.