h11-3 - subspace of U 5 Let V be the vector space over the...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
COT5615 Mathematics for Intelligent Systems Fall 2011 Home Work Assignment 3: Due Monday 10/31/11 before class In the problems below, the matrices A = 1 2 3 4 5 7 6 8 9 B = ± 1 2 3 4 5 6 ² 1. Hand compute the LU decomposition of A 2. Hand compute the QR decomposition of A . 3. Invert A using the solution of the first question above. 4. Considering B : U V as a linear transform, find the subset of U that maps to the zero vector in V . Prove that this subset is a
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: subspace of U . 5. Let V be the vector space over the complex numbers of all functions from R into C , i.e., the space of all complex-valued functions on the real line. Let f 1 ( x ) = 1 ,f 2 ( x ) = e ix ,f 3 ( x ) = e-ix . Prove that f 1 ,f 2 ,f 3 are linearly independent. Let g 1 ( x ) = 1 ,g 2 ( x ) = cos x,g 3 ( x ) = sin x . Find an invertible 3 × 3 matrix P such that g j = 3 X i =1 P ij f i . 1...
View Full Document

This note was uploaded on 01/22/2012 for the course COP 5615 taught by Professor Staff during the Fall '08 term at University of Florida.

Ask a homework question - tutors are online