Matrices--#5

Question

The size of two matrices A and B are given. Find the sizes of the Product AB and the product BA, whenever these products exist.

A is 5X3, and b is 3X1.

Find the size of the product AB.

Answer 1

You have to make sure the number of columns of the 1st matrix = the number of rows of the 2nd matrix.

 

Matrix A has 5 rows and 3 columns.

Matrix B has 3 rows and 1 column.

 

The product AB is defined because the A has 3 columns and B has 3 rows.  To find the new dimensions,

(5 x 3)(3 x 1) = (5 x 1), 5 rows and 1 column

 

The product BA is not defined because B has 1 column and A has 5 rows.  You can't dimension match as we did in the previous example.