Matrix Multiplication

Matrix Multiplication

Here is a step by step guide to multiply matrices. The exercises can help you measure your knowledge of matrix multiplication.

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.

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. \(\begin{bmatrix}(-5)(-2)+(-5).3 & (-5)(-3)+(-5).5 \\(-1)(-2)+2.3 & (-1)(-3)+2.5 \end{bmatrix}=\begin{bmatrix}-5 & -10 \\8 & 13 \end{bmatrix}\)

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. \(\begin{bmatrix}(-4).0+(-6)(-3)+(-6).0 \\0.0+6(-3)+3.0 \end{bmatrix}=\begin{bmatrix}18 \\-18 \end{bmatrix}\)

Example 3:

\(\begin{bmatrix}1 & 3 \\2 & 4 \end{bmatrix}\)\(\begin{bmatrix}2 &4 \\-2 & 1 \end{bmatrix}\)

Solution:

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

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. \(\begin{bmatrix}2(-2)+(-1)(-1)+(-1) .4\\3(-2)+1 .(-1)+5 .4 \end{bmatrix}=\begin{bmatrix}-7 \\13 \end{bmatrix}\)

Exercises

Solve.

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

Related to "Matrix Multiplication"

Grade 3 MCAS Math Worksheets
Grade 3 MCAS Math Worksheets
FREE Grade 6 OST Math Practice Test
FREE Grade 6 OST Math Practice Test
MAP Math Grade 8 Practice Test Questions
MAP Math Grade 8 Practice Test Questions
Top 10 Grade 4 MAP Math Practice Questions
Top 10 Grade 4 MAP Math Practice Questions
Full-Length ASVAB Math Practice Test-Answers and Explanations
Full-Length ASVAB Math Practice Test-Answers and Explanations
Full-Length ASVAB Math Practice Test
Full-Length ASVAB Math Practice Test
SBAC Grade 4 Math FREE Sample Practice Questions
SBAC Grade 4 Math FREE Sample Practice Questions
Grade 3 PSSA Math Worksheets
Grade 3 PSSA Math Worksheets
FREE Grade 8 NYSE Math Practice Test
FREE Grade 8 NYSE Math Practice Test
NYSE Math Grade 8 Practice Test Questions
NYSE Math Grade 8 Practice Test Questions

Leave a Reply

Your email address will not be published. Required fields are marked *

How Does It Work?

Find Books

1. Find eBooks

Locate the eBook you wish to purchase by searching for the test or title.

add to cart

2. Add to Cart

Add the eBook to your cart.

checkout

3. Checkout

Complete the quick and easy checkout process.

download

4. Download

Immediately receive the download link and get the eBook in PDF format.

Why Buy eBook From Effortlessmath?

Save money

Save up to 70% compared to print

Instantly download

Instantly download and access your eBook

help environment

Help save the environment

Access

Lifetime access to your eBook

Test titles

Over 2,000 Test Prep titles available

Customers

Over 80,000 happy customers

Star

Over 10,000 reviews with an average rating of 4.5 out of 5

Support

24/7 support

Anywhere

Anytime, Anywhere Access

Find Your Test

Schools, tutoring centers, instructors, and parents can purchase Effortless Math eBooks individually or in bulk with a credit card or PayPal. Find out more…