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

7 years agodarn I meant A = [ 3 7] [ 0 0]

7 years agoC = [ 0 1] [ 0 2 ]

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

7 years agoAre you asking in general, or in this specific case?

7 years agoin this specific case?

7 years agobut AC is not =0 here

7 years agoYes 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.

7 years agoif A is invertible I don't know how to show that

7 years agoA is not invertible

7 years agoC is not invertible

7 years agoI realize that A is not invertible too

7 years agoBut okay for C though do you know what it means by C=0

7 years agoDo they mean C is a 2 by 2 zero matrix?

7 years agoyou have C={0 1} {0 2}

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

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

7 years agobut 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?

7 years agoIts from a book

7 years agoI guess thanks for your help anyways

7 years agoso 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?

7 years agowhat is the name of the book?

7 years agoYes they gave me those two

7 years agoContemporary Linear Algebra

7 years agoHere's the exact question

7 years agorobert busby?

7 years agoWe 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

7 years agoYeah

7 years agoand then they gave those two matrices in the example 3

7 years agowhat section

7 years ago3.2 number 30

7 years agoYou have the book?

7 years agodarn it sometimes you go through most of the book on amazon.com

7 years agowell there's not much other information than what I've have provided

7 years agoYeah I can't get it to become invertible so I'll just leave it

7 years agoThanks for your help

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

7 years agoYeah alright night!

7 years agonight

7 years agoI 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

7 years ago