Exercise 2.1.47 Prove that ifA^-1 exists and AX=0 then X =0.

Question

asked May 15, 2020 199k views

1 Answer

PhilDin · Answer 1 · 2020-05-22T01:11:15+0000

Answer:

Explanation:

If
A^(-1) exist, then we have that
$A^(-1)\cdot A=1$ .

Therefore, in the case that
AX=0 , if we multiply both

terms in the equation by
A^(-1) , then we have

$A \cdot A^(-1)X=A^(-1)0$

and so the equation tells us that

$X=A\cdot A^(-1)X=A^(-1)0=0$ .