Answer to Question #345526 in Linear Algebra for Tee

Question

suppose that A,B,C and D are matrices with the following sizes: A(5 x 2) B(4 x 2) C(4 x 5) D(4 x 5)

determine in each of the following case whether a product is defined. if it is so then give the size of the resulting matrix.

i) BD

ii) AC - B

iii) DC + A

Answer 1

You can only multiply two matrices if their dimensions are compatible , which means the number of columns in the first matrix is the same as the number of rows in the second matrix.

So, in first case (i) the product is undifined B has 2 column and D has 4 rows. $2\ne4$ ;

(ii) same, A has 2 column and C has 4 rows, so we can't multiply them;

(iii) here the product DC also is undifined, science D has 5 columns and C has 4 rows.