Ma1bAnHw4

# Ma1bAnHw4 - → V be the linear transformation f x,y =(3 x...

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

CALIFORNIA INSTITUTE OF TECHNOLOGY Department of Mathematics Math 1b, Analytical; Homework Set 4 Due: 10am, Monday, February 4, 2008 Read sections 17 and 18 from Chapter 2 of Apostol. That is read pages 58 through 65. You can collaborate on the problems as long as you write up all solutions in your own words and understand those solutions. Remember to justify all your answers. 1. Let V = V 2 be the space of ordered pairs of real numbers, X = { e 1 ,e 2 } the basis of coordinate vectors, where e 1 = (1 , 0) and e 2 = (0 , 1), and let f : V
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: → V be the linear transformation f ( x,y ) = (3 x + 2 y, 5 x + y ) (1) What is the null space of f ? (2) What is the matrix m X ( f ) of f with respect to the basis X ? What is m X ( f 2 )? (3) Let Y = { (1 , 2) , (2 , 3) } . Find the matrices m Y ( f ) and m Y ( f 2 ). 2. Problem 4 on page 50 of Apostol. In addition ﬁnd the matrices of T and T 2 with respect to the basis { i + j , i-j } . 3. Problem 6 on page 67 of Apostol. 4. Problem 9 on page 67 of Apostol. 1...
View Full Document

## This note was uploaded on 04/28/2010 for the course MATH 1B taught by Professor Aschbacher during the Winter '07 term at Caltech.

Ask a homework question - tutors are online