Let A be a 3 × 4 matrix, B be a 4 × 5 matrix, and C be a 4×4 matrix. Determine which of the following products are defined and find the size of those that are defined.

a) AB

b) BA

c) AC

d) CA

e) BC

f) CB

Step 1</p>

Given that A is a matrix, B is a and C is a

In this problem we are asked to define which of the following are defined and we have to find the size of those defined products.

Step 2</p>

We can say that a product of 2 matrices is defined if and only if the number of columns of the first matrix is equal to the number of rows of the second matrix.

Then the product matrix will have the same number of rows as the first matrix and the same number of columns as the 2nd matrix.

Example.

If and

Therefore is defined only when .

And XY will be an matrix.

Step 3</p>

a) AB

AB is defined and is a matrix.

Step 4</p>

b) BA

BA is not defined since the number of column in B is not equal to the number of rows in A