If you did the early homework, you don't need to turn in problems 9, 19, or 21 from section 5.1, problem 7 from section 5.2, or problem 14 from section 5.3 on Monday. However, please make a note that you have done so. Question 1:

Let K=

1 2 2 1

.

Compute the characteristic polynomial &chi_K(t) of K.
Question 2: Compute the matrix &chi_K(K). (Use the convention that constants in a polynomial correspond to multiples of the identity matrix. Thus if p(t)=t+4, p(A)=A+4I.)
Formulate a conjecture about the value of &chi_A(A), for general square matrices A. (Do not attempt to prove your conjecture.)

Question 3: Find a matrix P and a diagonal matrix D such that K=PDP^-1, or determine that they don't exist.

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