Question

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

Answer 1

Answer:

Step-by-step 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

$X=A\cdot A^{-1}X=A^{-1}0=0$.