0:00
Hello.
00:01
Okay, so here we consider the matrix a.
00:04
The matrix a here is equal to the matrix 6 negative 2, negative 2, 3.
00:12
And the objective here is to determine the spectral decomposition of this matrix.
00:19
So first, we want to write the characteristic equation of this matrix, which is just the determinant of lambda i minus a, setting that equal to zero.
00:29
So the determinant of also lambda i minus a that's going to give us lambda minus six and then two positive two positive two and then lambda minus three.
00:50
So determinant there is equal to just a zero matrix.
00:53
So we get then lambda squared minus nine lambda plus 14 is equal to zero, which we can then factor as lambda.
01:04
Minus 7 times lambda minus 2.
01:09
So lambda minus 7 times lambda minus 2 equals 0...