294.final.03

294.final.03 - Math 294 Final exam. Fall 2003. Do All 6...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 294 Final exam. Fall 2003. Do All 6 problems. Your must justify all your answers except for problem 6 which consists of a number of true or false questions. Points will be deducted for illegible writing. No calculators. 1a Find an orthornormal eigenbasis for the linear transformation 101 010 A = . (20pts) 1b Find m A x G , where 1 0 0 x ⎛⎞ ⎜⎟ = ⎝⎠ G and m is a positive integer. Express your answer in m . (10pts) 1c Solve dx Ax dt = G G , with initial condition 1 (0 ) 0 0 xt == G . (10pts) 1d For a n by n matrix A , A e is defined as 2 lim ..... 1! 2! ! k A n k AA A eI k →∞ ≡+ + + + . Evaluate A e for A in (1a). (10pts) 2. Let ( ( )) (3 1) Tfx f x =− be a linear transformation from 2 P to 2 P . 2a. Find the matrix A of T with respect to the basis { } 2 1, , x x B= . (10pt) 2b. Find all the eigenvalues and eigenvectors of T . Is T diagonalizable ? (20pts) 3 Find a matrix B representating V proj x G , where x G is a vector in 3 R and V is the subspace of 3 R defined by 12 3 20 xx x −+ = . (21pts) 4a. Let N P
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/10/2008 for the course MATH 2940 taught by Professor Hui during the Fall '05 term at Cornell.

Page1 / 3

294.final.03 - Math 294 Final exam. Fall 2003. Do All 6...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online