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Unformatted text preview: Diﬀerential Equations
Homework Assignment 5
Due on Thursday, February 24, at the start of the recitation you are registered in
Your homework should have a cover sheet with the following information: course title,
recitation, last and ﬁrst name (as they appear in the roster), number of homework. If you
use several sheets, please staple them. The problems should be written neatly and in the
order they were assigned. 111
Problem 1. Let A = 2 3 2 .
Determine whether A is invertible. If A is invertible, use Gaussian elimination to
compute its inverse.
Problem 2. Compute the determinant of the Vandermonde matrix 1 x x2
W = 1 y y 2 .
1 z z2
Simplify your answer.
Problem 3. Find the eigenvalues and eigenvectors of 300
A = 1 1 2 .
324 Problem 4. Find the eigenvalues and eigenvectors of 70 0
A = 0 0 −3 .
Problem 5. Find the eigenvalues and eigenvectors of 201
A = 0 5 0 .
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