# Math Help - matrices equation solution 71

1. ## matrices equation solution 71

if Ax=Bx then for every x vector in R^n then A=B

is it true?

2. True. If $A\neq B$ then $A-B=(c_{ij})\neq 0$ so, there exists $c_{kl}\neq 0$. Choose an adequate $x_0$ such that $(A-B)x_0\neq 0$ or equivalently $Ax_0\neq Bx_0$.

Regards.