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

Algebra.Com
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)   (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
RELATED QUESTIONS

what is the determinant of the matrix B= 6 6 2 1 4 3 7 3 6 5 3 0 6 3 0 7... (answered by Fombitz)
find the determinant of the matrix A=(9 6 2 1 2 3 4 5... (answered by Alan3354)
Reduce the following matrices to triangular form and find the rank. Also reduce the... (answered by lynnlo)
Please help me to find rank of matrix 1 2 3 4 2 4 6 8 -1 -2 -2... (answered by richwmiller)
Consider the accompanying matrix. Use the test for linear independence to find a basis... (answered by venugopalramana)
1)Find an LU factorization of the matrix A below. A= 1 4 -1 5 3 7 -2 9 (answered by richwmiller)
Find the inverse of each matrix, if it exists. 1.[ -2 -1] [10 7] 2.[-4 2]... (answered by Mathtut)
Find an LU factorization of the matrix A below. A= 1 4 -1 5 3 7 -2 9 (answered by hokies)
Solve this augmented matrix 5 -4 3|15 6 2 9| 13 7 6-6| 6 (answered by richwmiller)