What is the value of k
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What is the value of k

[From: ] [author: ] [Date: 11-10-12] [Hit: ]
For L to be real, the discriminate has to be greater than 0.......
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?

-
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
1
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