Given the sizes of two matrices A and B, determine the sizes of the product AB and the product BA, if the products are defined. Worth 8 points.

Question

Given the sizes of two matrices A and B, determine the sizes of the product AB and the product BA, if the products are defined. Worth 8 points.

(a) Ais4×4andBis4×4.

(b) Ais2×1andBis1×1.

(c) Ais2×3andBis3×2.

(d) Ais2×1andBis2×1.

Answer 1

In order to multiply two matrices, the number of columns in the first matrix must equal the number of rows in the second matrix.  The matrices you have listed here can be multiplied.

 

a)

 

AB = 4 × 4

 

BA cannot be multiplied.  First matrix B is  4 × 4. Second matrix A is  2 × 1.

 

4 does not equal 2.

 

 

b)

 

AB = 2 × 1

 

BA has no product.

 

 

Try the last two on your own.

Answer 2

For AB to produce a product and BA to produce a product, A and B must be square and of the same dimensions.

 

(a)