Evaluate the 3 × 3 determinant. Use the properties of determinants to your advantage.

Question

2	−1	6
0	6	1
1	−2	−1

Answer 1

Expanding off column 1:

| 6 1 | | -1 6 |

2 det | | + | |

| -2 -1 | | 6 1 |

note that the middle determinant off row 2 is gone because of the zero in row2 column1 ,and the coefficient of the third is 1 because of the 1 in row3 colum1

2 (-6 - -2) + (-1 - 36) =

2(-6 + 2) + (-37) =

2(-4) + (-37) =

-8 + -37

= -45