How Can You Represent a Linear Transformation with a Block Matrix Form?

[tiger2030]

Homework Statement

Let T: C→D with dim(A)=n and dim(B)=m. Show that there exists bases B and B' for C and D, respectively, such that the matrix of T in block form is

M=|I 0|
|0 0|

where I is a k by k identity matrix

Homework Equations

The Attempt at a Solution

Honestly no idea where or how to start. Just looking for some hints and guided questions

 

[maajdl]

What is the purpose of the "dim(A)=n" statement.
A is never used.
Could you check the problem statement?

 

[tiger2030]

Sorry for the mix up. It should be dim(C)=n and dim(D)=m

 

[tiger2030]

So there exists {u1,u2,...,un} such that for any c that's an element of C we can make a linear combination of {u1,...un} that equals c. Similarly for {v1,v2,...vm} for any d that's an element of D