A First Course in Linear Algebra
A First Course in Linear Algebra
Robert A. Beezer
University of Puget Sound
Version 3.40
Congruent Press
Robert A. Beezer is a Professor of Mathematics at the University of Puget Sound,
where he has been on the faculty sin

Homework 8
Ha Pham
November 20, 2008
Problem 1 (Chapter 6 - ex 24). Find a polynomial q P2 (R) such that
1
p( ) =
2
Z
1
p(x)q(x) dx()
0
for every p P2 (R).
Proof. Use G-S on the basis (1, x, x2 ) to obtain an orthonormal basis denoted by (1, p1 , p2 ),
th

Systems of Linear Equations
Howard Anton, Elementary Linear Algebra, 5th ed., Wiley, New York, 1987.
1. Solve the following systems using Gauss-Jordan elimination.
x1 + x2 + 2x3 = 8
(a.) x1 2x2 + 3x3 = 1
3x1 7x2 + 4x3 = 10
2x1 + 2x2 + 2x3 = 0
(b.) 2x1 + 5