Math 205a Quiz Worksheet - 2008 Page 2
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2Math 205A
Quiz 08 page 2
November 21, 2008
NAME
.
2
4
2. Find a 2 × 2 matrix A that has v =
and w =
as eigenvectors with associated eigenvalues
2
5
3 and 1, respectively. Show all your work, including any matrices you create in order to do this problem.
CIRCLE your final matrix A.
3. Mark each statement TRUE if it is always true, and FALSE if there are counter examples. Let A be
an n × n square matrix.
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a. A
exists ⇒ A is diagonalizable.
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b. A
exists ⇒ A does not have 0 as an eigenvalue.
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c. A is diagonalizable ⇒ A
exists.
d. If 0 is not an eigenvalue of A then A is not singular.
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