Rref Example 5 By L H D

The 4X4 Matrix below will be reduced to Reduced Row Echelon Form (RREF)

Matrix A:

1 2 1 2
3 5 2 1
4 6 2 1
3 2 1 0

Begin with 3 * R1 then R1-R2=R2 ==

1 2 1 2
0 1 1 5
4 6 2 1
3 2 1 0

4 * R1 then R1-R3=R3 ==

1 2 1 2
0 1 1 5
0 2 2 7
3 2 1 0

3 * R1 then R1-R4=R4 ==

1 2 1 2
0 1 1 5
0 2 2 7
0 4 2 6

2 * R2 then R2-R3=R3 ==

1 2 1 2
0 1 1 5
0 0 0 3
0 4 2 6

Permute R4 with R3 ==

1 2 1 2
0 1 1 5
0 4 2 6
0 0 0 3

R2 * 4 - R3 = R3 ==

1 2 1 2
0 1 1 5
0 0 2 14
0 0 0 3

R3/2=R3 ==

1 2 1 2
0 1 1 5
0 0 1 7
0 0 0 3

R4/3=R4 ==

1 2 1 2
0 1 1 5
0 0 1 7
0 0 0 1

R4 * -7 + R3 = R3 ==

1 2 1 2
0 1 1 5
0 0 1 0
0 0 0 1

R4 * -5 + R2 = R2 ==

1 2 1 2
0 1 1 0
0 0 1 0
0 0 0 1

R4 * -2 + R2 = R2 ==

1 2 1 0
0 1 1 0
0 0 1 0
0 0 0 1

R3 * -1 + R2 = R2 ==

1 2 1 0
0 1 0 0
0 0 1 0
0 0 0 1

R3 * -1 + R1 = R1 ==

1 2 0 0
0 1 0 0
0 0 1 0
0 0 0 1

R2 * -2 + R1 = R1 ==
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

You can check it in Matlab by entering the beginning matrix as:

A=[1 2 1 2;3 5 2 1;4 6 2 1;3 2 1 0]

Then enter:

rref(A)

The answer will be the end matrix restated below

1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

Hope this helps.

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