exam2Solutions

# Exam2Solutions - Math 222-500 Solutions Exam 2 1(15 Define the following a coordinates of a vector If V is a vector space and S u u U 1 u u U n is

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 222-500 Solutions Exam 2 November 21, 2006 1 . (15) Define the following: a . coordinates of a vector, If V is a vector space, and S u u U 1 , u , u U n is a basis of V , then the coordinates of a vector x U u V with respect to the basis S are the unique scalars c i , 1 U i U n such that x U u ¡ i u 1 n c i u U i . b . linear transformation, A linear transformation, L , from a vector space V to a vector space W is a function with domain V and codomain W , L : V ¡ W , such that L U u x U¢ U y U ¡ u u L U x U ¡ ¢ U L U y U ¡ , for all vectors x U and y U in V and any scalars u and U . c . orthonormal basis. Let V be a vector space with inner product ¢ , ¢ . An orthonormal basis is a basis u U 1 , u , u U n of V such that u U i , u U j u ¡ ij . 2 . (20) Let V u P 4 the vector space of polynomials of degree 3 or less. Let B 1 u t 2 u 2 t , 1 U t u t 3 , 2 u t U t 2 , 3 t U t 3 , B 2 u t u t 2 U t 3 , 1 U t u t 2 , 5 t U 7 t 2 , u 6 t U 5 t 3 . Find the change of basis matrix P such that u x ¡ U B 1 u P u x ¡ U B 2 . Let S u 1, t , t 2 , t 3 .Let P 1 and P 2 be change of basis matrices such that u x ¡ U S u P 1 u x ¡ U B 1 u x ¡ U S u P 2 u x ¡...
View Full Document

## This note was uploaded on 03/27/2008 for the course MATH 222 taught by Professor Stecher during the Spring '08 term at Texas A&M.

### Page1 / 5

Exam2Solutions - Math 222-500 Solutions Exam 2 1(15 Define the following a coordinates of a vector If V is a vector space and S u u U 1 u u U n is

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online