Thread: Matrix Arithmetic Help...

I am having two problems here. The first one I am somewhat confident of:

1. Show that in general, for any square matrix satisfying:

then


I proceeded as follows:




While what I did seems legitimate...how do I show that the matrices must be square?

2. Let A, D, and P be n X n matrices satisfying . Solve for A. Must it be true that A = D?

For this one I am not sure how to proceed. In order to get rid of P I need to say multiply by but that doesn't seem to help me... Same sort of situation for P.

Originally Posted by alterah

i am having two problems here. The first one i am somewhat confident of:

1. Show that in general, for any square matrix satisfying:

then


i proceeded as follows:




while what i did seems legitimate...how do i show that the matrices must be square? mr f says: Does a non-square matrix have an inverse ....?

2. Let a, d, and p be n x n matrices satisfying . Solve for a. Must it be true that a = d?

For this one i am not sure how to proceed. In order to get rid of p i need to say multiply by but that doesn't seem to help me... Same sort of situation for p.

2. ....


Edit: That annoying intermittent glitch that changes any posted upper case letter into a lower case letter appears to have struck again.

Wow...there are definitely those moments in math when you are like "How did I not simply see that I made the problem harder than it was. What is your input on the first problem? Thanks!

Originally Posted by Alterah

[snip]
What is your input on the first problem? Thanks!

I have already given my input (in the form of a question for you to ponder).

Whoops...didn't see the text...in red in your quote.