Question

1

3 1. Find the inverse using elementary matrices A 2-3 Find a sequence of elementary matrices whose product is the given matrix. 2-H 4 3 Find an LU-factorization. 3 01 6 1 1 3. -3 1

Answer 1

A nou A= IA thin afply Elementay toons formalion to make itI= A A We folowp - 2 A 1/3 R,R -213 R2-R2-R A 213 3 -213 R R,R A A I

Civen manx A 2 we knou I. fornding sequsnu elementary malix we duive e,,E2. Such that A= I A= Hert, e 8tart O 3 R2-5 R2-2 3R A = Nouw €2 than we A = M R, >-чR C Apain trun we ay -4 2 R, -R R Nouw

ay E O thiplyA €'e","e, Now €1 - V4 4equnu ot Matntes foutoizat en LU e C 3d 3 e 3 2 aef odt a. be+cf 3 Fquating 3e = =) e = '/3 3d o > d- 0 aet- >6- +f bd+c:I *) с - 1 O de 3 оо1 U: 3 -1 O 1 Dо |-3 C