Re: Matrices as Linear Maps

Quote:

Originally Posted by

**AllanCuz** Hey Team,

I'm not sure where to start on part a, but part b I think I have a decent start.

We know that A maps from Fn to Fm, and B maps from Fp to Fn. So we define the left multiplication of these guys as such,

So to find the range of AB we can let Z be some arbitrary vector in

and see for what values is it good for

We can note that

is a subset of

so the following inequality results,

We can further note that if

is a surjective map then its range is actually equal to

turning the inequality into equality.

Was the above process correct for b, and if so, are there any hints for a?

Thanks!

That looks right or me. For the second part, consider writing the matrix as a sum of column matrices.

Re: Matrices as Linear Maps

strictly speaking, such a sum does not exist, perhaps you meant a sum of matrices that are all 0's except for one column?

Re: Matrices as Linear Maps

Quote:

Originally Posted by

**Deveno** strictly speaking, such a sum does not exist, perhaps you meant a sum of matrices that are all 0's except for one column?

Obviously, I was letting the OP fill things in for themselves, you know?

Re: Matrices as Linear Maps

well you know me, i'm sorta slow-witted....