Question

Somebody help me with this LA question pls!
prove: Given that x is a vector,if Ax=0 and A has inverse A^-1, then x=0.

Answer 1

@amistre64

Answer 2

@xlegendx hey there do you have any idea?

Answer 3

vector algebra?

Answer 4

a better way to say is LA, Linear Algebra

Answer 5

A is a invertible matrix, square, non-singular, ofcuz

Answer 6

hmm i think @amistre64 would give a better explanation than I would though. Since he has 99 SmartScore. right @amistre64 ?

Answer 7

@amistre64 is a math genius I believe

Answer 8

99 is my IQ :)

Answer 9

c'mon, even me has an Iq over 100!

Answer 10

prove by contradiction is popular ...

spose all of it is true except for the x=0 part and show its absurdity

Answer 11

that would be tedious, right?

Answer 12

if A is invertible, then it has a linearly independant vector basis; determinant not zero

we are assuming A to be a square matrix right?

Answer 13

I found a solution ! if Ax=0, then A^-1*Ax=0, so I*x=0, thus x=0 @amistre64

Answer 14

Ax = 0

A'Ax = A'0

x = 0

since A is invertible it is not a zero matrix and would require the trivial coefficient vector X equal to 0,0,0,0,0,....

Answer 15

we used the same method

Answer 16

yes we did :) but we have to base it on previous thrms that state the nature of an invertible matrix

Answer 17

@amistre64 I just posted a question on the Lit section, would you go and have a look?

Answer 18

lit section? i doubt it