(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let B = (1 1 / -1 1)

That is a 2x2 matrix with (1 1) on the first row and (-1 1) on the second.

2. Relevant equations

3. 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 dont even know where to start.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# The Eigenvalues and eigenvectors of a 2x2 matrix

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