199k views
0 votes
Exercise 2.1.47 Prove that ifA^-1 exists and AX=0 then X =0.

1 Answer

3 votes

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.

User PhilDin
by
7.5k points

Related questions

asked Feb 14, 2024 14.8k views
Bettinna asked Feb 14, 2024
by Bettinna
8.1k points
1 answer
4 votes
14.8k views
asked Dec 16, 2024 207k views
DesperateLearner asked Dec 16, 2024
by DesperateLearner
8.3k points
1 answer
0 votes
207k views