MULTIPLYING MATRICES

Key Concept

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 :

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