Question

linear alebra

can you do problems 5&6 please.

5. If A is 2 by 3 and B is 3 by 2 ani AB = 1, show from its rank that BA 1. 3 points 6. Find the LU factorization of the matrix for the matrix A [10 points A=11-1 0 1-14 0 -4 What is the LDU factorization? Find the complete solution of Ar = b with b given above.

Answer 1

(5)

A is 2,3 matrix and B is 3,2 matrix so

is 2,2 and is 3,3 matrix .

Given that

$AB=I$

Since Rank of is 2 ,
rank(AB) 2

is 3,3 matrix, if

___(*

BA33-13,3 Rank (BA) 3.Rank I3)3

But we know that

$Rank(BA)\leq Rank(B)$____(1

and

B is 3,2 matrix so

___(2

Rank(B) < 2

By(1),(2)

___(**

Rank(BA) 2

By(*),(**) ,we can conclude that

$BA\not=I$