Prove that the reduced row echelon forms of the matricesleft

Phoebe 2021-03-08 Answered

Prove that the reduced row echelon forms of the matrices(1 1 4 8 0 1 11 2 3 9 0 5 20 2 2 2 1 14 31 4 1 11 0 13 4) (0 3 3 1 50 1 1 0 00 2 2 0 3)

are the two matrices. 

The point of the reduced row echelon form is that the corresponding system of linear equations is in a particularly simple form, from which the solutions to the system AX=C in (4) can be determined immediately.

 

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Expert Answer

coffentw
Answered 2021-03-09 Author has 103 answers

Step 1

First augmented matrix is: A=[1148011123905202221143141110134]

Now we use the fact that matrix A is row equivqlent to a matrix in reduced roe echelon form.

A=[1148011123905202221143141110134] R2  R2  R1 [1148011011104102221143141110134]

 

R4  R4  R1 [114801101110410222114303330123]

 

R1  R1  R2 [105703001110410222114303330123]

Step 2 

Now we will choose lower right submatrix and apply row operations. It is matrix:

A=[11104122211433330123]

Then:

A=[11104122211433330123] R2  R1 + R2 [11104100011613330123] 

R3  R3  3R1 [11104100

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