WINTER 2007 assign6-sol

WINTER 2007 assign6-sol - Math 235 Assignment 6 Due 9:15am,...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 235 Assignment 6 Due 9:15am, Wednesday March 7, 2007. 1. From the Text 6.2 #10. Show that { u 1 , u 2 , u 3 } is orthogonal basis for R 3 . Then express x as a linear combination of the u s. u 1 = 3- 3 , u 2 = 2 2- 1 , u 3 = 1 1 4 , x = 5- 3 1 . Solution. u 1 u 2 = u 1 T u 2 = 3 * 2 + (- 3) * 2 + 0 * (- 1) = 0 u 1 u 3 = u 1 T u 3 = 3 * 1 + (- 3) * 1 + 0 * 4 = 0 u 2 u 3 = u 2 T u 3 = 2 * 1 + 2 * 1 + (- 1) * 4 = 0 Thus { u 1 , u 2 , u 3 } is an orthogonal set. Since the set consists of linearly independent vectors, the three vectors form a basis for R 3 . x = x u 1 u 1 u 1 u 1 + x u 2 u 2 u 2 u 2 + x u 3 u 3 u 3 u 3 = 5 * 3 + (- 3) * (- 3) + 1 * 3 * 3 + (- 3) * (- 3) + 0 * u 1 + 5 * 2 + (- 3) * 2 + 1 * (- 1) 2 * 2 + 2 * 2 + (- 1) * (- 1) u 2 + 5 * 1 + (- 3) * 1 + 1 * 4 1 * 1 + 1 * 1 + 4 * 4 u 3 = 4 3 u 1 + 1 3 u 2 + 2 3 u 3 ....
View Full Document

Page1 / 4

WINTER 2007 assign6-sol - Math 235 Assignment 6 Due 9:15am,...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online