Given the matrix A=begin{bmatrix}0 & 0&1 0 & 3&0 1&0 & -10 end{bmatrix} and suppose that we have the following row reduction to its PREF B A=begin{bma

rocedwrp 2021-01-22 Answered
Given the matrix
A=[0010301010]
and suppose that we have the following row reduction to its PREF B
A=[0010301010][1010030001][1010010001][100010001]
Write A and A1 as product of elementary matrices.
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Expert Answer

broliY
Answered 2021-01-23 Author has 97 answers

Given the matrix
A=[0010301010]
Write A and A1 as product of elementary matrices. Step 2 Take the matrix A and exchange the first and second rows. Let E1 be the elementary row matrix corresponding to the above row operation.
E1=[001010100]
Notice that E1A=[1010030001]
Step 3 Next, take the matrix [1010030001] and divide the second row by the scalar 3. Let E2 be the elementary row matrix corresponding to the above row operation.
E2=[1000130001]
Notice that E2[1010030001]=[1010010001]
Step 4
Next, take the matrix [1010010001] and add 10 times the third row to the first row. Let E3 be the elementary row matrix corresponding to the above row operation.
E3=[1010010001]
Notice that E3[1010010001]=[100010001]=I
Step 5
Now,
I=E3[1010010001]=E3E2[1010030001]=E3E2E1A
and so A1=E3E2E1 , that is
A1=[1010010001][10100130001][001010100]
Step 6
Also,
A=E11E21E31
=

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Jeffrey Jordon
Answered 2022-01-30 Author has 2087 answers

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