00:01
Okay, so let's get an idea, first of all, what is a singular matrix? a singular matrix is a square matrix whose determinant is zero.
00:17
I'm just going to write det for determinant.
00:21
Okay, so we've got this matrix a here, and i understand that your problem, you want to find out where it's non -singular.
00:32
Let's look at where it's singular first.
00:36
So a is singular when the determinant equals 0.
00:49
Now what is the determinant of this matrix? well, it's a 2 by 2.
00:54
And so we multiply the diagonal, which is 7 times negative 1, and then we subtract that from the other diagonal, the super diagonal i think they call it.
01:06
And so the determinant of a is going to be negative 7 minus x.
01:12
So a is singular if the determinant equals 0.
01:21
So if this is equal to 0, and now if i add x to both sides of this equation, i have x equals negative 7.
01:33
So a is singular when x is equal to negative 7.
01:40
So a is not singular.
01:42
A is non -singular when x is not equal to negative 7...