00:01
So in this question, we want to know, are the following matrices invertible? so what we're going to do is we're going to find the determinant of each of these matrices.
00:09
If the determinant is zero, the matrix is not invertible.
00:15
If the determinant is anything besides zero, then the matrix is invertible.
00:22
So our first matrix, negative one, five, four, four.
00:26
If i want the determinant of this matrix, we take negative one times four, negative four minus four times five is 20.
00:44
That's negative 24, which is not zero.
00:50
And so yes, this is invertible.
00:53
If i look at number two, if i take the determinant of the matrix, seven negative seven, negative 21, 21, what do we get? seven times 21, 147 minus negative seven times negative 21, 147.
01:17
That is equal to zero.
01:20
Since the determinant is zero, this is not invertible.
01:25
No, there is no inverse.
01:28
Number three, we've got the matrix negative 21, negative seven, zero, zero.
01:34
So we're going to take the determinant of this matrix.
01:43
Negative 21 times zero is zero...