FinalTestReviewSpring2011

# pts solution deta i 0 0 0 we have two eigenvalues

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 ￿ −3￿1 ￿ 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 −...
View Full Document

## This document was uploaded on 02/19/2014 for the course MATH 441 at WVU.

Ask a homework question - tutors are online