hi to all : ))(adsbygoogle = window.adsbygoogle || []).push({});

(excuse me for my english ^^')

I need help and I hope you can give me an hand, i must proof the null-rank theorem using block matrices but i can't resolve it.

This are the information in my possession:

I have the a function

f: R^n --->R^m

x --->y=Ax

I must reorder columns of the matrix A (m*n) and write A as:

(A1 A2)

(A3 A4)

where:

A1 is (r*r) with rankA=r

A2 is (r*q) with q=n-r

A3 is (p*r) with p=m-r

A4 is (p*q)

then resolving this linear sistem:

(A1 A2) (x1) = (c)

(A3 A4) (x2) (d)

I would find a proof for the null rank theorem.

Can someone help me pls? thk : ))

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Need help: Proof Null-rank theorem with block matrices

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**