Calculate Eigenvalues of a 2x2 Matrix | A, E, I | Eigenvectors | Eigenspace

[thomas49th]

Homework Statement

Let A =
a b
c d
A characteristic value of A (often called an eigenvalue) is denoted by λ and satisfies the relation

det(A - λI) = 0

Obtain the characteristics values of E =
1 -1
-1 1

Homework Equations

Well I is the unit or identity matrix

1 0
0 1

The Attempt at a Solution

I don't understand how E can be of any relation to what the question is asking. Does E = A?

det(A - λI) = 0

=> a - λ, b
c, d - λ = 0

super. ad + λ² - λa - λd + bc = 0

Let's presume for a second that their asking me that A = E

that means a=1, b = -1,c = -1,d = 1

=> 1 + λ² - λ(1-1) + 1 = 0
=? λ² = -2

that canny be though can it?

Any suggestions are welcomed!

Thanks
Tom

 

[Mark44]

Yes, they want the solutions of the equation |E - $\lambda$I| = 0

I get different eigenvalues, both real. Check your determinant work.

 

[thomas49th]

ahh, my bad

x² - 2x = 0

=> x(x-2)

therefore, x = 0, 2

Is that what you got?

Thanks :)
Tom

 

[Mark44]

You lost your equation. x(x - 2) = 0, which allows you to say x = 0 or x = 2.

ahh, my bad

x² - 2x = 0

=> x(x-2)

therefore, x = 0, 2

Is that what you got?

Thanks :)
Tom