SOLUTION: rank of the matrix ⎡ 4 5 6 7 3 4 5 6 2 3 4 5 1 2 3 4

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Question 557397: rank of the matrix ⎡
4 5 6 7
3 4 5 6
2 3 4 5
1 2 3 4
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
4 5 6 7
3 4 5 6
2 3 4 5
1 2 3 4

Multiply row 2 by -1 and add it to row 1

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

Multiply row 3 by -1 and add it to row 2

1 1 1 1
1 1 1 1
2 3 4 5
1 2 3 4

Multiply row 4 by -1 and add it to row 3

1 1 1 1
1 1 1 1
1 1 1 1
1 2 3 4

Multiply row 1 by -1 and add it to row 2

1 1 1 1
0 0 0 0
1 1 1 1
1 2 3 4

Multiply row 1 by -1 and add it to row 3

1 1 1 1
0 0 0 0
0 0 0 0
1 2 3 4

Swap rows 2 and 4

1 1 1 1
1 2 3 4
0 0 0 0
0 0 0 0

Multiply row 1 by -1 and add it to row 2

1 1 1 1
0 1 2 3
0 0 0 0
0 0 0 0

Multiply row 2 by -1 and add it to row 1

1 0 -1 -2
0 1  2  3
0 0  0  0
0 0  0  0

That's in row reduced echelon form.  The number of
not-all-zero rows is 2, so its rank is 2.

Edwin