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Unformatted text preview: Nam: _ ID Number: TA Name: " ' I Section: "THU: Niath 20F. Exam 3 December 5, 2007 No calculators or any other devices are aiiomrrd on this exam. I'Vrite your solutions cleri'i‘iy and legibiy; no audit will be given for iliegibiu solutions.
Read each question carefully. If any question is not clear. as}: for clariﬁcation.
Answer each question completely, and show all your work. 2 l: U
1. Consider the matrix A z 2 k 1
t i 1 (a) (15 points) Does there exist a value of it such that A is not invertible? If your
answer is yes, explain why and find all these values of k; if your answer is no,
explain why. (1)} (15 points) Find all numbers is such that the determinant of the matrix A satisﬁes
the equation: clet{AB) = l, where A"! :: AA. bu, 2 (25 points) Find every eigenvalue and every eigenspaee 0f the matrix A below. State the
algebraic multiplicity of each eigenvalue, and state the dimension of each eigenspaee. —400
.4: 510
H521 T 3. (20 points) Is the matrix :1 below diagonalizable’? If your answer is yes‘ ﬁnd a diagonal
matrix D and an invertible matrix P such that A = PDP‘I. If your answer is no‘
then give :1 reason for this answer. A: com
own—A
l MI— 4. (a) (15 points) Find a ‘2 x 2 diagonal matrix D and a 2 X 2 invertible matrix P such that. A = PEP“.
4_ 2 1 I ._ '_
. {a 1]. _ (b) {10 points) Compute the matrix A? ...
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This note was uploaded on 07/25/2009 for the course MATH 20F taught by Professor Buss during the Winter '03 term at UCSD.
 Winter '03
 BUSS
 Math

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