This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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? ...
View
Full Document
 Winter '03
 BUSS
 Math

Click to edit the document details