Answer to Question #156472 in Linear Algebra for Hhhh

Question

1 2 0 -1

2 6 -3 -3

3 10 -6 -5

Find the rank

Answer 1

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.