The matrix A=
1 k
-1 6
has two distinct real eigenvalues if and only if k<_____
can anyone show me how to do this?
1 k
-1 6
has two distinct real eigenvalues if and only if k<_____
can anyone show me how to do this?
-
A - LI = 0, I = unit matrix..
The poor man's lambda (L) is used here..
Find the determinate of..
| 1 - L K |
| -1 6 - L|
=0
(1 - L)(6 - L) + k = 0
L^2 - 7L + 6 + k = 0
For L to be real, the discriminate has to be greater than 0.
b^2 - 4ac = 49 - 4(6 + k) > 0
25 > 4k
k < 25/4
The poor man's lambda (L) is used here..
Find the determinate of..
| 1 - L K |
| -1 6 - L|
=0
(1 - L)(6 - L) + k = 0
L^2 - 7L + 6 + k = 0
For L to be real, the discriminate has to be greater than 0.
b^2 - 4ac = 49 - 4(6 + k) > 0
25 > 4k
k < 25/4