Question

求A的秩（3 1 0 4 1 2 -1 3 0 2 1 2 -3 4 -1 5 0 3 4 3 -1 2 2 7 0）

Answer 1

3 1 0 4 1

2 -1 3 0 2

1 2 -3 4 -1

5 0 3 4 3

-1 2 2 7 0

r1r3

1 2 -3 4 -1

2 -1 3 0 2

3 1 0 4 1

5 0 3 4 3

-1 2 2 7 0

r2-2r1,r3-3r1,r4-5r1,r5+r1

1 2 -3 4 -1

0 -5 9 -8 4

0 -5 9 -8 4

0 -10 18 -16 8

0 4 -1 11 -1

r4-2r2,r3-r2

1 2 -3 4 -1

0 -5 9 -8 4

0 0 0 0 0

0 0 0 0 0

0 4 -1 11 -1

r3r5

1 2 -3 4 -1

0 -5 9 -8 4

0 4 -1 11 -1

0 0 0 0 0

0 0 0 0 0

所以秩为3