Let A=begin{bmatrix}1 & 2 -1 & 1 end{bmatrix} text{ and } C=begin{bmatrix}-1 & 1 2 & 1 end{bmatrix}a)Find elementary matrices E_1 text{ and } E_2 such that C=E_2E_1Ab)Show that is no elementary matrix E such that C=EA

Khadija Wells 2020-12-07 Answered

Let A=[1211] and C=[1121]
a)Find elementary matrices E1 and E2 such that C=E2E1A
b)Show that is no elementary matrix E such that C=EA

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Expert Answer

mhalmantus
Answered 2020-12-08 Author has 106 answers

Step 1
Consider the given information,
A=[1211] and C=[1121]
a)
now, calculate the elementary matrices.
The matrix C can be be calculated by A by the following operations.
Step 2
Interchange the Rows of the matrix A. Then,
A=[1112]
Now, multiply -1 in the row one and add in second.
A=[1121]
Then the elementary matrix are defined as,
E1=[0110]
And
E2=[1011]
Step 3
(b) It can be observed from part a. A and C lines above are equivalent. However, none of the 2 matrices A and C can be changed to another by a single row operation. Hence there is no primary matrix E such that C=EA.

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Jeffrey Jordon
Answered 2022-01-27 Author has 2064 answers

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