Mathematics
OpenStudy (anonymous):

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

8 years ago
OpenStudy (anonymous):

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

8 years ago
OpenStudy (anonymous):

C = [ 0 1] [ 0 2 ]

8 years ago
OpenStudy (anonymous):

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

8 years ago
OpenStudy (anonymous):

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

8 years ago
OpenStudy (anonymous):

in this specific case?

8 years ago
OpenStudy (anonymous):

but AC is not =0 here

8 years ago
OpenStudy (anonymous):

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.

8 years ago
OpenStudy (anonymous):

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

8 years ago
myininaya (myininaya):

A is not invertible

8 years ago
myininaya (myininaya):

C is not invertible

8 years ago
OpenStudy (anonymous):

I realize that A is not invertible too

8 years ago
OpenStudy (anonymous):

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

8 years ago
OpenStudy (anonymous):

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

8 years ago
myininaya (myininaya):

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

8 years ago
OpenStudy (anonymous):

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

8 years ago
OpenStudy (anonymous):

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

8 years ago
myininaya (myininaya):

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?

8 years ago
OpenStudy (anonymous):

Its from a book

8 years ago
OpenStudy (anonymous):

I guess thanks for your help anyways

8 years ago
myininaya (myininaya):

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?

8 years ago
myininaya (myininaya):

what is the name of the book?

8 years ago
OpenStudy (anonymous):

Yes they gave me those two

8 years ago
OpenStudy (anonymous):

Contemporary Linear Algebra

8 years ago
OpenStudy (anonymous):

Here's the exact question

8 years ago
myininaya (myininaya):

robert busby?

8 years ago
OpenStudy (anonymous):

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

8 years ago
OpenStudy (anonymous):

Yeah

8 years ago
OpenStudy (anonymous):

and then they gave those two matrices in the example 3

8 years ago
myininaya (myininaya):

what section

8 years ago
OpenStudy (anonymous):

3.2 number 30

8 years ago
OpenStudy (anonymous):

You have the book?

8 years ago
myininaya (myininaya):

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

8 years ago
OpenStudy (anonymous):

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

8 years ago
OpenStudy (anonymous):

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

8 years ago
OpenStudy (anonymous):

8 years ago
myininaya (myininaya):

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

8 years ago
OpenStudy (anonymous):

Yeah alright night!

8 years ago
myininaya (myininaya):

night

8 years ago
OpenStudy (anonymous):

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

8 years ago