MULTIPLYING MATRICES

Key Concept

multiplyingmatrices

Examples 1-6 : In each case, find the product.

Example 1 :

Solution :

Number of columns of the first matrix = 2

Number of rows of the second matrix = 2

Since the number of columns of the first matrix and number of rows of the second matrix are equal, the above two matrices can be multiplied.

Example 2 :

Solution :

Number of columns of the first matrix = 2

Number of rows of the second matrix = 2

Since the number of columns of the first matrix and number of rows of the second matrix are equal, the above two matrices can be multiplied.

Example 3 :

Solution :

Number of columns of the first matrix = 1

Number of rows of the second matrix = 1

Since the number of columns of the first matrix and number of rows of the second matrix are equal, the above two matrices can be multiplied.

Example 4 :

Solution :

Number of columns of the first matrix = 2

Number of rows of the second matrix = 2

Since the number of columns of the first matrix and number of rows of the second matrix are equal, the above two matrices can be multiplied.

Example 5 :

Solution :

Number of columns of the first matrix = 3

Number of rows of the second matrix = 3

Since the number of columns of the first matrix and number of rows of the second matrix are equal, the above two matrices can be multiplied.

Example 6 :

Solution :

Number of columns of the first matrix = 3

Number of rows of the second matrix = 2

Since the number of columns of the first matrix and number of rows of the second matrix are NOT equal, the above two matrices can NOT be multiplied.

Example 7 :

For the above two matrices A and B, find AXB and BXA and check if AXB = BXA.

Solution :

A X B :

Number of columns of matrix A = 2

Number of rows of matrix B = 2

Since the number of columns of matrix A and number of rows of matrix B are equal, we can find AXB.

B X A :

Number of columns of matrix B = 2

Number of rows of matrix A = 2

Since the number of columns of matrix B and number of rows of matrix A are equal, we can find BXA.

From (1) and (2),

A X B ≠ B X A

From this, we can conclude that matrix multiplication is not commutative.

Example 8 :

Find the value of x :

Solution :

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. SAT Math Resources (Videos, Concepts, Worksheets and More)

    Oct 06, 24 05:49 AM

    SAT Math Resources (Videos, Concepts, Worksheets and More)

    Read More

  2. Digital SAT Math Problems and Solutions (Part - 50)

    Oct 06, 24 05:44 AM

    digitalsatmath44.png
    Digital SAT Math Problems and Solutions (Part - 50)

    Read More

  3. Digital SAT Math Problems and Solutions (Part - 49)

    Oct 04, 24 09:58 AM

    Digital SAT Math Problems and Solutions (Part - 49)

    Read More