Quiz 2

Problem 1: Calculate the determinant of the matrix A.

1) Factor A = P L U

P

L

U

Note: Other factorings are possible!

2) Calculate Det(A) by Det(A) = Det(P) Det(L) Det(U)

Problem 2: The Cayley-Hamilton Theorem

The characteristic polynomial of a square matrix A is found by

The Cayley-Hamilton Theorem states that

Given

1) Calculate

is called the characteristic polynomial of the matrix A.

2) Show

Calculate:

is: