Answer to Question #190365 in Linear Algebra for Regomoditswe Dibob

Question

Assume that A and B are matrices of the same size. Determine an expression for A if 2A − B = 5(A + 2B).

Answer 1

$Solution: Given ~that, A ~and~ B~ are~ matrices ~of~ the ~same~ size. Addition ~and ~subtraction \\of ~the ~ given ~ matrices ~are ~possible. \\\therefore 2A − B = 5(A + 2B) \\~~2A-B=5A+10B \\~2A-5A=10B+B \\~~~~~~~-3A=11B \\~~~~~~~~ ~~\therefore A=-\frac{11}{3} B \\Which ~is ~ the~ expression ~for~ A.$