Answer to Question #191351 in Linear Algebra for peter

Question

Suppose that A, B, C, and D are matrices with the following sizes: A (5 × 2), B (4 × 2), C (4 × 5), D (4 × 5) Determine in each in each of the following case whether a product is defined. If it is so, then give the size of the resulting matrix.

(i) DC,

(ii) −CA + B,

(iii) CD − D

Answer 1

(i) DC does not exist because (D(4*5))5 is not equal to 4(C(4*5))

(ii) −CA + B exists because -C(4*5)*A(5*2)=G(4*2),G(4*2)+B(4*2)=F(4*2),4*2

(iii) CD - D, does not exist because (C(4*5))5 is not equal to 4(D(4*5))