1.5-1.6

# 1.5-1.6 - MATH321 – HOMEWORK SOLUTIONS HOMEWORK #2...

This preview shows pages 1–2. 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: MATH321 – HOMEWORK SOLUTIONS HOMEWORK #2 Section 1.5: Problems 1, 2(d)(e), 3, 4, 8 Section 1.6: Problems 1, 2(a)(b), 3(a), 4, 5, 9, 13, 14, 17 Krzysztof Galicki Problem 1.5.1 (See Answers to Selected Exercises ). Problem 1.5.2 (a) Linearly dependent. The second matrix A 2 is obtained from the first one A 1 by multiplying with -2. Hence, 2 A 1 + A 2 = O . (d) Linearly independent. We write a ( x 3- x ) + b (2 x 2 + 4) + c (- 2 x 3 + 3 x 2 + 2 x + 6) = 0 . ( a- 2 c ) x 3 + (2 b + 3 a ) x 2 + (- a + 2 c ) x + 4 b + 6 c = 0 . This is easily seen to have only trivial solutions. a = 2 c but 2 b =- 3 a =- 3 c which makes a = c . Put together this implies that a = b = c = 0. Problem 1.5.3 The sum of the first three matrices equals to the sum of the last two. Hence, the set is linearly dependent. Problem 1.5.4 We have a 1 e 1 + ··· a n e n = a 1 (1 , ,..., 0) + ··· a n (0 ,..., , 1) = ( a 1 ,a 2 ,...,a n ) = (0 ,..., 0) which can happen if and only if a 1 = a 2 = ··· = a n = 0. Hence, the set { e 1 ,...,e n } is linearly independent in F n (for any field F )....
View Full Document

## This note was uploaded on 11/30/2009 for the course MATH 115A taught by Professor Liu during the Winter '07 term at UCLA.

### Page1 / 4

1.5-1.6 - MATH321 – HOMEWORK SOLUTIONS HOMEWORK #2...

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

View Full Document
Ask a homework question - tutors are online