This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math/CSE 6643 Exam Fall 2010 Name: Put your name on all sheets now. 80 minutes, 8 questions for 80 points total. No calculators, electronic devices, books, or notes are permitted. Use a pen, put a box around your final answers, and cross out anything that is not to be graded. No credit is given for answers without the reasoning that leads to them: show all work . If you need more space, continue onto the back (and write that you have done so at the bottom of the front side). 1. (10 points) Find the rankone matrix which is the best approximant to A = 2 1 0 1 in the matrix 2 norm. A * A = 2 0 1 1 2 1 0 1 = 4 2 2 2 . λ 2 6 λ + 4 = 0 ,λ = 3 ± √ 5. A * A = V Σ 2 V * , σ 1 = p 3 + √ 5. v 1 in kernel of 1 √ 5 2 2 1 √ 5 so v 1 = [1 + √ 5 , 2] T / p 10 + 2 √ 5. Av 1 = σ 1 u 1 . The best rank1 approximation is σ 1 u 1 v T 1 = Av 1 v T 1 = 2 1 0 1 6 + 2 √ 5 2 + 2 √ 5 2 + 2 √ 5 4 1 10 + 2 √ 5 = 14 + 6 √ 5 8 + 4 √ 5 2 + 2 √ 5 4 1 10 + 2 √ 5 1 Math/CSE 6643 Exam Fall 2010...
View
Full
Document
This note was uploaded on 12/25/2011 for the course MATH 6643 taught by Professor Staff during the Fall '08 term at Georgia Tech.
 Fall '08
 Staff
 Math, Linear Algebra, Algebra

Click to edit the document details