Math 205a,b Quiz 8 Worksheet - Linear Algebra - 2013
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1MATH 205A,B - LINEAR ALGEBRA
WINTER 2013
QUIZ 8
NAME:
Section:(Circle one)
A(1 : 10)
B(2 : 40)
Show ALL your work CAREFULLY.
Let
3
0 0
2 5 3
A =
.
8
1 3
(a) The matrix A has 3 as one of its eigenvalues. Find the other eigenvalues of A.
(b) Find a basis for the eigenspace of A corresponding to the eigenvalue λ = 3.
(c) Determine the rank of the matrix (A
3I). [Hint: what is the dimension of the eignespace as
in part (b)?] Justify your answer.
Date: March 13, 2013.
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