This preview shows pages 1–7. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Let A = 1 1 0 1 0 0 , ~ b = 1 1 1 . (a) Determine ~x * which minimizes k A~x~ b k among all ~x R 2 . (b) Let S be an orthogonal 3 3 matrix. Determine the leastsquare solution of the linear system SA ~x = S ~ b . 5. (a) (15 points) Let ~v 1 , ~v 2 be a bases of R 2 and T : R 2 R 2 a linear transformation with T ( ~v 1 ) = ~v 1 + ~v 2 T ( ~v 2 ) = ~v 1~v 2 . Determine the matrix of the 4fold composition T 4 in the standard bases of R 2 . (b) (5 points) Consider the 2 n 2 n block matrix A = 1 n1 n where 1 n stands for the n n identity matrix. Is A invertible? 6. (15 points) You are given a noninvertible 3 3 matrix A with three eigenvalues. You are told that the diagonal elements of A are a 11 =2 , a 22 = 0 , a 33 = 7. Prove that at least one of the eigenvalues of A must be greater or equal to 5 2 ....
View
Full
Document
 Spring '08
 Staff
 Math, Linear Algebra, Algebra

Click to edit the document details