If you did the early homework by 5:00 Wednesday, you don't need to turn in problems 3 or 28 from section 5.4, problems 10 or 25 from section 5.5, or problem 4 from section 5.7 on Friday. Question 1:

Let L=

0 1 1 1

, let v1=

2 1-&radic(5)

, v2=

2 1+&radic(5)

, and v0=

0 1

.

L has eigenvalues t₁=½(1-&radic(5)) and t₂=½(1+&radic(5)), with corresponding eigenvectors v₁ and v₂.
Given that 2&radic(5) * v₀= v₂-v₁, find a formula for Lⁿv₀. [Leave your answer in terms of t₁, t₂, v₁, v₂, and n.]
Question 2: Let D:P₄->P₃ be the derivative. You proved in calculus that D is a linear transformation. Find the matrix for D in terms of the bases {1, t, t², t³, t⁴} and {1, t, t², t³}.
Question 3:

Let O=

1 -2 1 3

, P=

-1+i -1-i 1 1

, and D=

2+i 0 0 2-i

.

Given that O=PDP^-1, find real-valued matrices B and C such that O=BCB^-1 and C is of the form

C=

a -b b a

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