Question

The sizes of two matrices A and B are given. Find the sizes of the product AB and the product BA, if the products are defined. A is 4 × 2, B is 2 × 4.

Answer 1

Answer:

AB: size 4 x 4

BA: size 2 x 2

Step-by-step explanation:

When we want to multiply two matrices, we need first to check if the number of columns of the first matrix is equal the number of rows of the second matrix. Then, the resulting matrix would have the number of rows equal the number of rows of the first matrix, and the number of columns equal the number of columns of the second matrix.

That is, if we have a matrix A with dimensions a x b and a matrix B with dimensions c x d, to calculate the product AB we must have b = c, and the resulting product would have dimensions a x d.

Finally, if A is 4 x 2 and B is 2 x 4, we would have:

AB = (4 x 2) (2 x 4)

2 = 2 -> product is possible.

Dimensions of the result: 4 x 4

BA = (2 x 4) (4 x 2)

4 = 4 -> product is possible.

Dimensions of the result: 2 x 2