Question #156472
1 2 0 -1
2 6 -3 -3
3 10 -6 -5
Find the rank
Expert's answer
To solve this task we have to make this matrix in echelon form. For this reason let's use elementary operations
From the second row we have to subtract the 2 times first row; from the third row we have to subtract the 3 times first row.
/ \
| 1 2 0 -1 |
| 0 2 -3 -1 |
| 0 4 -6 -2 |
\ /
let's divide the second row by 2
/ \
| 1 2 0 -1 |
| 0 2 -1.5 -0.5 |
| 0 4 -6 -2 |
\ /
from the third row we have to subtract the 4 times second row
/ \
| 1 2 0 -1 |
| 0 2 -1.5 -0.5 |
| 0 0 0 0 |
\ /
Because we have 2 non-zero rows, the rank of matrix is 2.
