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Mathematics 44 Online
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?

OpenStudy (anonymous):

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

OpenStudy (anonymous):

C = [ 0 1] [ 0 2 ]

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

in this specific case?

OpenStudy (anonymous):

but AC is not =0 here

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.

OpenStudy (anonymous):

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

myininaya (myininaya):

A is not invertible

myininaya (myininaya):

C is not invertible

OpenStudy (anonymous):

I realize that A is not invertible too

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

myininaya (myininaya):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

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?

OpenStudy (anonymous):

Its from a book

OpenStudy (anonymous):

I guess thanks for your help anyways

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?

myininaya (myininaya):

what is the name of the book?

OpenStudy (anonymous):

Yes they gave me those two

OpenStudy (anonymous):

Contemporary Linear Algebra

OpenStudy (anonymous):

Here's the exact question

myininaya (myininaya):

robert busby?

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

OpenStudy (anonymous):

Yeah

OpenStudy (anonymous):

and then they gave those two matrices in the example 3

myininaya (myininaya):

what section

OpenStudy (anonymous):

3.2 number 30

OpenStudy (anonymous):

You have the book?

myininaya (myininaya):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (anonymous):

Thanks for your help

myininaya (myininaya):

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

OpenStudy (anonymous):

Yeah alright night!

myininaya (myininaya):

night

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

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