Two m x n matrices A and B are called EQUIVALENT (writen A ~e B if there exist invertible matracies U and V (sizes m x m and n x n) such that A = UBV(adsbygoogle = window.adsbygoogle || []).push({});

a) prove the following properties of equivalnce

i) A ~e A for all m x n matracies A

ii) If A ~e B, then B ~e A

iii) A ~e B and B~e C, then A~e C

--------------

Lets just do part i) for now...

It seems ovicus that "A ~e A for all m x n matracies A"... but.. heres how i would do it

A = m x n

U = m x m

V = n x n

So

A = UAV

A = (UA)V UA = (m X m)(m X n) = (m X n)

A = (UA)(V) UAV = (m X n)(n x n) = (m x n)

A = A

How does that sound? Is that how you prove this? Or do i have the wrong idea?

Please help

thanks

**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!

# Homework Help: Linear Algebra: The vector space R and Rank

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