Question

Show that if A is invertible and AC =0 then C=0; similarly if C is invertible and AC=0 then A=0?

Answer 1

darn I meant A = [ 3 7]
[ 0 0]

Answer 2

C = [ 0 1]
[ 0 2 ]

Answer 3

C was originally that but I don't know if I am suppose to make it all zeroes

Answer 4

Are you asking in general, or in this specific case?

Answer 5

in this specific case?

Answer 6

but AC is not =0 here

Answer 7

Yes it is, it becomes a zero matrix. But they want me to show that C can also be a zero matrix and when multiplied with A will give a zero matrix as well.

Answer 8

if A is invertible I don't know how to show that

Answer 9

A is not invertible

Answer 10

C is not invertible

Answer 11

I realize that A is not invertible too

Answer 12

But okay for C though do you know what it means by C=0

Answer 13

Do they mean C is a 2 by 2 zero matrix?

Answer 14

you have C={0 1}
{0 2}

Answer 15

Yeah but the question say show that if A is invertible and AC=0 then C=0

Answer 16

I can't show that A is invertible thats why I'm lost

Answer 17

but A isn't invertible
AC={3 7} * {0 1} ={3*0+7*0 3*1+7*2}={0 17}
{0 0} {0 2} {0*0+0*0 0*1+0*2} {0 0}
im sorry but this case does not go with the above question?
first of all it isn't invertible
someting is wrong with your question
it makes no sense
second of all AC does not equal zero
are these matrices the book or teacher gave you?

Answer 18

Its from a book

Answer 19

I guess thanks for your help anyways

Answer 20

so this wasn't some general thing you are suppose to prove right?
the book actually gives you 2 matrices and tells you to do the above?

Answer 21

what is the name of the book?

Answer 22

Yes they gave me those two

Answer 23

Contemporary Linear Algebra

Answer 24

Here's the exact question

Answer 25

robert busby?

Answer 26

We showed in Ex. 3 that its possible to have nonzero matrices A and C for which AC=0. However show that if A is invertible and AC=0 then C=0; similarly if C is invertible and AC =0 then A=0

Answer 27

Yeah

Answer 28

and then they gave those two matrices in the example 3

Answer 29

what section

Answer 30

3.2 number 30

Answer 31

You have the book?

Answer 32

darn it sometimes you go through most of the book on amazon.com

Answer 33

well there's not much other information than what I've have provided

Answer 34

Yeah I can't get it to become invertible so I'll just leave it

Answer 35

Thanks for your help

Answer 36

im sorry
ask your teach
i like linear algebra
but for that case the question made no sense

Answer 37

Yeah alright night!

Answer 38

night

Answer 39

I think theree's some confusion here. Ignore the specific matrices. The question is IN General, prove if A invertible and AC=0 then C=0:

left multiply by A^-1 then AC = 0 becomes A^-1AC=0 which becomes C=0

Similarly for A if C invertible