Sol34 - Partial Solution Set Leon 3.4 3.4.3 Given the vectors x 1 =(2 1 T x 2 =(4 3 T and x 3 =(7 3 T(a Show that x 1 and x 2 form a basis for R

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: Partial Solution Set, Leon § 3.4 3.4.3 Given the vectors x 1 = (2 , 1) T , x 2 = (4 , 3) T , and x 3 = (7 ,- 3) T , (a) Show that x 1 and x 2 form a basis for R 2 . (b) Why must x 1 , x 2 , and x 3 be linearly dependent? (c) What is the dimension of Span( x 1 , x 2 , x 3 )? Solution : (a) This follows because they are (by inspection) linearly independent in R 2 . Since the dimension of R 2 is 2, x 1 and x 2 form a basis for R 2 . (b) Since R 2 is 2-dimensional, any collection of more than two vectors from R 2 must be linearly dependent. (c) Since x 1 and x 2 form a basis for R 2 , the dimension of Span( x 1 , x 2 , x 3 ) is 2, i.e., Span( x 1 , x 2 , x 3 ) = R 2 . 3.4.4 Given the vectors, x 1 = (3 ,- 2 , 4) T , x 2 = (- 3 , 2 ,- 4) T , and x 3 = (- 6 , 4 ,- 8) T , what is the dimension of Span( x 1 , x 2 , x 3 )? Solution : Both x 2 and x 3 are scalar multiples of x 1 , so the dimension of Span( x 1 , x 2 , x 3 ) is 1. 3.4.5 Given the vectors, x 1 = (2 , 1 , 3) T , x 2 = (3 ,- 1 , 4) T , and x 3 = (2 , 6 , 4) T , (a) Show that x 1 , x 2 , and x 3 are linearly dependent. (b) Show that x 1 and x 2 are linearly independent. (c) What is the dimension of Span( x 1 , x 2 , x 3 )?...
View Full Document

This note was uploaded on 07/17/2011 for the course MATH 311 taught by Professor Anshelvich during the Spring '08 term at Texas A&M.

Page1 / 3

Sol34 - Partial Solution Set Leon 3.4 3.4.3 Given the vectors x 1 =(2 1 T x 2 =(4 3 T and x 3 =(7 3 T(a Show that x 1 and x 2 form a basis for R

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