 # 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)Find elementary matrices such that $C={E}_{2}{E}_{1}A$
b)Show that is no elementary matrix E such that $C=EA$

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Step 1
Consider the given information,

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,
${A}^{\ast }=\left[\begin{array}{cc}-1& 1\\ 1& 2\end{array}\right]$
Now, multiply -1 in the row one and add in second.
${A}^{\ast }=\left[\begin{array}{cc}-1& 1\\ 2& 1\end{array}\right]$
Then the elementary matrix are defined as,
${E}_{1}=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$
And
${E}_{2}=\left[\begin{array}{cc}1& 0\\ -1& 1\end{array}\right]$
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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