Practice Final 1

Practice Final 1 - Math 20F Final Exam 11:30 AM March 21,...

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

View Full Document Right Arrow Icon
Math 20F Final Exam 11:30 AM March 21, 2003 There are a total of 80 points possible. TWO PAGES of notes are allowed. No calculators are allowed. You must show your work to receive credit. 1. (12 pts) (a) Find the eigenvalues of the matrix 120 030 004 . (b) Find an eigenvector for each eigenvalue. 2. (12 pts) Let W be the subspace of R 5 spanned by 1 2 0 2 0 , 2 - 1 0 0 2 and 0 2 0 - 2 1 . (a) Find an orthonormal basis for W . (b) Write (9 , 99 , 9 , 9) T as a sum of a vector in W and a vector in W . 3. (6 pts) L (( a, b, c ) T )= ax ( x - 1) + bx + c defines a linear transformation L from R 3 to P 3 . Find a matrix for L using the standard basis for R 3 and the basis 1, x , x 2 for P 3 . 4. (12 pts) A matrix A R 4 × 4 has eigenvalues 1, - 1, 2 and 3. What are the eigenvalues and determinants of the following matrices? (i) A - 1 (ii) A T (iii) A 2 - A .
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 04/16/2008 for the course MATH 20F taught by Professor Buss during the Fall '03 term at UCSD.

Page1 / 2

Practice Final 1 - Math 20F Final Exam 11:30 AM March 21,...

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