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.

How to Multiply Matrix? (+FREE Worksheet!)

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. \(\begin{bmatrix}(-5)(-2)+(-5)(3) & (-5)(-3)+(-5)(5) \\(-1)(-2)+(2)(3) & (-1)(-3)+(2)(5) \end{bmatrix}= \begin{bmatrix}(10)+(-15) & (15)+(-25) \\(2)+(6) & (3)+(10) \end{bmatrix}=\begin{bmatrix}-5 & -10 \\8 & 13 \end{bmatrix}\)

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:

\(\begin{bmatrix}(1) (2)+(3)(-2) & (1) (4)+(3) (1) \\(2) (2)+ (4)(-2) & (2) (4)+(4) (1) \end{bmatrix}=\begin{bmatrix}(2)+(-6) & (4)+(3) \\(4)+ (-8) & (8)+(4) \end{bmatrix}=\begin{bmatrix}-4 & 7 \\-4 & 12 \end{bmatrix}\)

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.

  1. \(\color{blue}{\begin{bmatrix}0 & 2 \\-2 & -5 \end{bmatrix}\begin{bmatrix}6 & -6 \\3 & 0 \end{bmatrix}}\)
  2. \(\color{blue}{\begin{bmatrix}3 & -1 \\-3 & 6\\-6&-6 \end{bmatrix}\begin{bmatrix}-1 & 6 \\5 & 4\end{bmatrix}}\)
  3. \(\color{blue}{\begin{bmatrix}0 & 5 \\-3 & 1\\-5&1 \end{bmatrix}\begin{bmatrix}-4 & 4 \\-2 & -4\end{bmatrix}}\)
  4. \(\color{blue}{\begin{bmatrix}5 & 3&5 \\1 & 5&0 \end{bmatrix}\begin{bmatrix}-4 & 2 \\-3 & 4\\3&-5 \end{bmatrix}}\)
  5. \(\color{blue}{\begin{bmatrix}4 & 5 \\-4 & 6\\-5&-6 \end{bmatrix}\begin{bmatrix}4 & 6 \\6& 2\\-4&1 \end{bmatrix}}\)
  6. \(\color{blue}{\begin{bmatrix}-2 & -6 \\-4 & 3\\5&0 \\4&-6\end{bmatrix}\begin{bmatrix}2 & -2&2 \\-2 &0&-3 \end{bmatrix}}\)
  1. \(\color{blue}{\begin{bmatrix}6 & 0 \\-27 & 12 \end{bmatrix}}\)
  2. \(\color{blue}{\begin{bmatrix}-8 & 14 \\33 & 6\\ -24&-60\end{bmatrix}}\)
  3. \(\color{blue}{\begin{bmatrix}-10 & -20 \\10 & -16\\ 18&-24\end{bmatrix}}\)
  4. \(\color{blue}{\begin{bmatrix}-14 & -3 \\-19 & 22 \end{bmatrix}}\)
  5. \(\color{blue}{Undefined}\)
  6. \(\color{blue}{\begin{bmatrix}8 & 4&14\\-14 & 8&-17\\10&-10&10 \\20&-8&26\end{bmatrix}}\)

Related to "How to Multiply Matrix? (+FREE Worksheet!)"

How to Determine Limits Using the Squeeze Theorem?How to Determine Limits Using the Squeeze Theorem?
How to Determine Limits Using Algebraic Manipulation?How to Determine Limits Using Algebraic Manipulation?
How to Estimate Limit Values from the Graph?How to Estimate Limit Values from the Graph?
Properties of LimitsProperties of Limits
How to Find the Expected Value of a Random Variable?How to Find the Expected Value of a Random Variable?
How to Define Limits Analytically Using Correct Notation?How to Define Limits Analytically Using Correct Notation?
How to Solve Multiplication Rule for Probabilities?How to Solve Multiplication Rule for Probabilities?
How to Solve Venn Diagrams and the Addition Rule?How to Solve Venn Diagrams and the Addition Rule?
How to Find the Direction of Vectors?How to Find the Direction of Vectors?
Vectors IntroductionVectors Introduction

What people say about "How to Multiply Matrix? (+FREE Worksheet!)"?

No one replied yet.

Leave a Reply