HOW TO MULTIPLY MATRICES

Find each product, if possible.

Problem 1 :

Solution:

• Dimension of first matrix is 1 x 2
• Dimension of second matrix is 2 x 2
• The product is defined and dimension of product matrix will be 1 x 2.

Problem 2 :

Solution:

• Dimension of first matrix is 2 x 1
• Dimension of second matrix is 1 x 3
• The product is defined and dimension of product matrix will be 2 x 3.

Problem 3 :

Solution :

• Dimension of first matrix is 2 x 3
• Dimension of second matrix is 2 x 2
• The product is not defined since the number of columns in the first matrix and number of rows in the second matrix is not equal.

It is not possible.

Problem 4 :

Solution:

• Dimension of first matrix is 2 x 2
• Dimension of second matrix is 2 x 1
• The product is defined and the order of the product matrix is 2 x 1.

Find each product, if possible.

Problem 5 :

Solution:

• Dimension of first matrix is 1 x 2
• Dimension of second matrix is 2 x 1
• The product is defined and the order of the product matrix is 1 x 1.

Problem 6 :

Solution:

• Dimension of first matrix is 2 x 2
• Dimension of second matrix is 2 x 2
• The product is defined and the order of the product matrix is 2 x 2.

Problem 7 :

Solution:

• Dimension of first matrix is 2 x 3
• Dimension of second matrix is 2 x 2
• The product is not defined.

Problem 8 :

Solution:

• Dimension of first matrix is 2 x 3
• Dimension of second matrix is 3 x 1
• The product is defined and the order of product matrix is 2 x 1.

Problem 9 :

Solution:

Problem 10 :

Solution:

It is not possible.

Problem 11 :

Solution:

Problem 12 :

Solution: