Let A=begin{pmatrix}2 &1 6 & 4 end{pmatrix} a) Express A^{-1} as a product of elementary matrices b) Express A as a product of elementary matrices

Cabiolab 2020-11-17 Answered
Let A=(2164)
a) Express A1 as a product of elementary matrices
b) Express A as a product of elementary matrices
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Expert Answer

Adnaan Franks
Answered 2020-11-18 Author has 92 answers
Step 1
Given: A=(2164)
a) Express A1 as a product of elementary matrices
b) Express A as a product of elementary matrices
Step 2
[2164][1001]R2:R23R1[1001]R2:R23R1=[1031]E
=[2101][1031]R2:R2÷2=[1/2001]E2
=[11/201][1/2031]R1=R1R22[1001]R1:R1R22=[11/201]E3
=[1001][21/231]
E3E2E1A=I
E3E2E1I=A1
you can recheck it
A1=E3E2E1=[11/201][1/2001][1031]
=[11/201][1/2031]=[1/23/231]
=[21/231]
Step 3
(A1)1=(E3E2E1)1
A=E11E21E31
E1=[1031],E11=11[1031]
E2=[1/2001],E21=11/2=[1001/2]
E3=[11/201],E31=11=[11/201]
Jeffrey Jordon
Answered 2022-01-24 Author has 2064 answers

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