Practice Final 1

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

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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 .

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## This note was uploaded on 04/16/2008 for the course MATH 20F taught by Professor Buss during the Fall '03 term at UCSD.

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

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