WEBVTT

1
00:00:00.000 --> 00:00:05.863
Here is the problem: [[-3, 2, negative 5], [-7, negative 1, negative 6], [-9, 2, 3]].

2
00:00:06.313 --> 00:00:09.808
Find the determinant of a 3 times 3 matrix.

3
00:00:10.608 --> 00:00:12.860
Read the 3 times 3 matrix.

4
00:00:13.310 --> 00:00:16.410
Expand along the first row (cofactor expansion).

5
00:00:16.860 --> 00:00:19.101
Evaluate each 2 times 2 minor.

6
00:00:19.551 --> 00:00:22.848
Combine with the alternating signs plus minus +.

7
00:00:23.648 --> 00:00:27.294
So the answer is det(A) equals 238.

8
00:00:27.744 --> 00:00:35.813
The determinant is 238, which is non-zero, so the matrix is invertible and its rows are linearly independent.

9
00:00:36.613 --> 00:00:42.789
Computed exactly with fractions; row reduction gives the same value 238.