Hi guys, I need help with transforming a matrix to reduced row echelonform. Give

Question

Hi guys,

I need help with transforming a matrix to reduced row echelonform.
Given the following:
1 0 1 1 -1
0 1 1 2 1
1 1 2 1 -2

I tried to solve it, I came up with the following:

R1=R1-R3
1 0 1 -1 -3
1 0 1 1 -1
0 1 1 2 1

R2=R2-R3
1 0 1 -1 -3
0 -1 0 -1 -2
0 1 1 2 1

R3= R2+R3
1 0 1 -1 -3
0 -1 0 -1 -2
0 0 1 1 -1

R1=R1-R3
1 0 0 -2 -2
0 1 0 1 2
0 0 1 1 -1

The solution provided is:
1 0 1 0 -2
0 1 1 0 -1
0 0 0 1 1

1. Can anybody solve it for me?
2. I have a question about the row operations. It is okay to dorepetitive transformations. For example,
in the way I solved it, I did R1=R1=R3 twice (one at the beginningand the other at the end)
3. Can anybody give me tips on how to do the reduced row echelonform. I find it hard to
transform it.

Explanation / Answer

R2<->R3
10 1 1 -1 11 2 1 -2 01 1 2 1
R1<->R2
1 1 2 1 -2
1 0 1 1 -1
0 1 1 2 1

R1=R1-R3
1 0 1 -1 -3
1 0 1 1 -1
0 1 1 2 1

R2=R2-R1 (from here on out our solution is different).
1 0 1 -1 -3
0 0 0 2 2
0 1 1 2 1
R2<->R3 1 0 1 -1 -3 0 1 1 2 1 0 0 0 2 2
R3=1/2R3 1 0 1 -1 -3 0 1 1 2 1 0 0 0 1 1
R2=R2-2R3 1 0 1 -1 -3 0 1 1 0 -1 0 0 0 1 1
R1=R1+R3 1 0 1 0 -2 0 1 1 0 -1 0 0 0 1 1

The trick is to be very careful with your row operations.Remember, to obtain rref: 1)each of your leading row elements must be 1s and have zeros in therows below, 2)the next row's leading row element must be to the right of andbelow the leading element in the previous row and there must beonly zeros to the left. 10 1 1 -1 11 2 1 -2 01 1 2 1
R1<->R2
1 1 2 1 -2
1 0 1 1 -1
0 1 1 2 1

R1=R1-R3
1 0 1 -1 -3
1 0 1 1 -1
0 1 1 2 1

R2=R2-R1 (from here on out our solution is different).
1 0 1 -1 -3
0 0 0 2 2
0 1 1 2 1
R2<->R3 1 0 1 -1 -3 0 1 1 2 1 0 0 0 2 2
R3=1/2R3 1 0 1 -1 -3 0 1 1 2 1 0 0 0 1 1
R2=R2-2R3 1 0 1 -1 -3 0 1 1 0 -1 0 0 0 1 1
R1=R1+R3 1 0 1 0 -2 0 1 1 0 -1 0 0 0 1 1

The trick is to be very careful with your row operations.Remember, to obtain rref: 1)each of your leading row elements must be 1s and have zeros in therows below, 2)the next row's leading row element must be to the right of andbelow the leading element in the previous row and there must beonly zeros to the left. 1 0 1 1 -1
0 1 1 2 1

R1=R1-R3
1 0 1 -1 -3
1 0 1 1 -1
0 1 1 2 1

R2=R2-R1 (from here on out our solution is different).
1 0 1 -1 -3
0 0 0 2 2
0 1 1 2 1
R2<->R3 1 0 1 -1 -3 0 1 1 2 1 0 0 0 2 2
R3=1/2R3 1 0 1 -1 -3 0 1 1 2 1 0 0 0 1 1
R2=R2-2R3 1 0 1 -1 -3 0 1 1 0 -1 0 0 0 1 1
R1=R1+R3 1 0 1 0 -2 0 1 1 0 -1 0 0 0 1 1

The trick is to be very careful with your row operations.Remember, to obtain rref: 1)each of your leading row elements must be 1s and have zeros in therows below, 2)the next row's leading row element must be to the right of andbelow the leading element in the previous row and there must beonly zeros to the left.
R1=R1-R3
1 0 1 -1 -3
1 0 1 1 -1
0 1 1 2 1

R2=R2-R1 (from here on out our solution is different).
1 0 1 -1 -3
0 0 0 2 2
0 1 1 2 1
R2<->R3 1 0 1 -1 -3 0 1 1 2 1 0 0 0 2 2
R3=1/2R3 1 0 1 -1 -3 0 1 1 2 1 0 0 0 1 1
R2=R2-2R3 1 0 1 -1 -3 0 1 1 0 -1 0 0 0 1 1
R1=R1+R3 1 0 1 0 -2 0 1 1 0 -1 0 0 0 1 1

The trick is to be very careful with your row operations.Remember, to obtain rref: 1)each of your leading row elements must be 1s and have zeros in therows below, 2)the next row's leading row element must be to the right of andbelow the leading element in the previous row and there must beonly zeros to the left.

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