MHB LU Factorization - Solve with Carter Barker

[cbarker1]

Dear Everyone,
I have some trouble with LU-Factorization. The problem work is below:
Original Matrix

First row- 3,0,1
2nd row- 6,1,1
3rd row- -3,1,0

Elementary Matrix 1
1st- 1,0,0
2nd- 0,1,0
3rd- 0,0,1
Switch R1 to R3

1st- 0,0,1
2nd- 0,1,0
3rd- 1,0,0​

The row operation:
Interchange R1 and R3

1st- -3,1,0
2nd- 6,1,1
3rd- 3,0,1

Elementary 2
1st- 1,0,0
2nd- 0,1,0
3rd- 0,0,1

Multiply -1/3R1

1st- -1/3,0,0
2nd- 0,1,0
3rd- 0,0,1​

The Row Operation
Multiplying -1/3 R1

1st- 1, -1/3, 0
2nd- 6, 1, 1
3rd- 3,0,1

Elementary 3

1st- 1,0,0
2nd- 0,1,0
3rd- 0,0,1

-6R1+R2

1st- 1,0,0
2nd- -6,1,0
3rd- 0,0,1​

The Row Operation
-6R1+R2

1st- 1,-1/3,0
2nd- 0,-1,1
3rd- 3,0,1

Elementary 4
1st-1,0,0
2nd- 0,1,0
3rd- 0,0,1

-3R1+R3
1st-1,0,0
2nd-0,1,0
3rd- -3,0,1

​

Row Operation
-3R1+R3

1st- 1,-1/3,0
2nd-0, -1, 1
3rd- 0, 1, 1

Elementary 5
1st- 1,0,0
2nd- 0,1,0
3rd- 0, 0,1

R2+R3

1st- 1,0,0
2nd- 0,1,0
3rd- 0,1,1

​

Row Operation:
R2+R3

1st- 1,-1/3,0
2nd- 0,-1,1
3rd- 0,0,2

Did I make a mistake somewhere? Thank you,

Carter Barker

 

[Prove It]

Dear Everyone,

I have some trouble with LU-Factorization. The problem work is below
Elementary Matrix

In first row- 3,0,1
1st- 1,0,0 1st- 0,0,1
2nd row- 6,1,1 2nd- 0,1,0 2nd- 0,1,0 Switch R1 to R3
3rd row- -3,1,0 3rd- 1,0,0
Elementary Matrix
1st- 1,0,0
2nd- 0,1,0
3rd- 0,0,1

1st- 0,0,1
2nd- 0,1,0 Switch R1 to R3

The row operation:
Interchange R1 and R3

1st- -3,1,0 1st- 1,0,0 1st- -1/3,0,0 Multiplying by -1/3 R1
2nd- 6,1,1 2nd- 0,1,0 2nd- 0,1,0
3rd- 3,0,1 3rd- 0,0,1 3rd- 0,0,1

The Row Operation
Multiplying -1/3 R1

1st- 1, -1/3, 0 1st- 1,0,0 1st- 1,0,0 -6R1+R2
2nd- 6, 1, 1 2nd- 0,1,0 2nd- -6,1,0
3rd- 3,0,1 3rd- 0,0,1 3rd- 0,0,1

The Row Operation
-6R1+R2

1st- 1,-1/3,0 1st 1,0,0 1st- 1,0,0 -3R1+R3
2nd- 0,-1,1 2nd 0,1,0 2nd- 0,1,0
3rd- 3,0,1 3rd 0,0,1 3rd- -3,0,1

Row Operation
-3R1+R3

1st- 1,-1/3,0
2nd-0, -1, 1
3rd- 0, -1, 1 Did I made a mistake somewhere? Thank you,

Carter Barker

From what you have written, I can't even tell what your starting matrix that you are trying to find the LU composition of is...