- #1
LydiaSylar
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Homework Statement
Let B = (1 1 / -1 1)
That is a 2x2 matrix with (1 1) on the first row and (-1 1) on the second.
Homework Equations
The Attempt at a Solution
A)
(1 1 / -1 1)(x / y) = L(x / y)
L(x / y) - (1 1 / -1 1) (x / y) = (0 / 0)
({L - 1} -1 / 1 {L-1}) (x / y) = (0 / 0)
Det (LI - B) = ({L - 1} -1 / 1 {L-1}) = 0
({L - 1} {L-1}) - (1)(-1)
L^2 -2L +2 = 0
L= 1 - i
= 1+i
So when L = 1-i
({1 -i - 1} -1 / 1 {1 -i -1})
(-i -1 / 1 -i)
-ix - y = 0
x - iy = 0
let x = t
t - iy = 0
y = t/i
Im not sure if that even makes sense. Or how I would continue.
B) Write the eigenvalues L of B in the form w = re^i(theta)
If someone could just give me a little nudge in the right direction for this one because I don't even know where to start.