Hello.
I have had some trouble solving the following problem.
The question asks to determine all values for β which A has distinct real eigenvalues.
This is what I have done so far.
|A-λI| = 0
=>(-2-λ)(-3-λ) - β = 0
Now my thinking was that If β =0 => λ = -3, -2
And if β =6 => λ2+5λ=0
=> λ(λ+5)=0
=> λ=0,-5
That is all I can think of for now. But this does not seem right.
I am sure that I have not covered all the possible values for β.
If someone can point out to me how to get all the possible values for β it would be much appreciated.
Thanks
I have had some trouble solving the following problem.
| -2 | β | |
| 1 | -3 | |
The question asks to determine all values for β which A has distinct real eigenvalues.
This is what I have done so far.
|A-λI| = 0
| -2-λ | β ....| = 0 |
| 1 | -3-λ | |
=>(-2-λ)(-3-λ) - β = 0
Now my thinking was that If β =0 => λ = -3, -2
And if β =6 => λ2+5λ=0
=> λ(λ+5)=0
=> λ=0,-5
That is all I can think of for now. But this does not seem right.
I am sure that I have not covered all the possible values for β.
If someone can point out to me how to get all the possible values for β it would be much appreciated.
Thanks