Unformatted text preview: g exercises. Show your work. (No credit will be given for an answer with
no supporting work shown.)
Ex. 1.
(a) State the Cofactor Formula for ﬁnding the inverse A−1 = [xij ] of an n × n matrix
A = [aij ].
C ji
(?? pts) Solution: xij = det(A) , where Cji = (−1)j +i det(Mji ) and Mji is obtained
from A by removing its j th row and ith column. 1200
3 4 0 0 (b) Use the Cofactor Formula you citated in (a) to ﬁnd x21 , if A = 0 0 5 0 .
0007
1 2 0 0
1
2 0 0
3 4 0 0 −31
0 −2 0 0
r
= −2 · 35.
(?? pts) Solution: det(A) =
=
0 0 5 0
0
0 5 0
0 0 0 7
0
0 0 7
3 0 0
C12
C12 = (−1)1+2 0 5 0 = −3 · 35. So, x21 = det(A) = −3··35 = 1.5
−2 35
0 0 7 1 134
Ex. 2. Find all eigenvalues and associated eigenvectors of the matrix A = 0 0 1 .
000
Is matrix A diagonalizable?
1−λ 3
4
−λ 1 = (1 −...
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This document was uploaded on 02/19/2014 for the course MATH 441 at WVU.
 Spring '08
 STAFF
 Math, Linear Algebra, Algebra

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