1.6 - Linear Algebra -115 Solutions to Fourth Homework...

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: Linear Algebra -115 Solutions to Fourth Homework Problem 2( d ) (Section 1 . 6) By Corollary 2 (page 47 in textbook) if a set is linearly independent and contains exactly n vectors, where n = dim( V ), then it is a basis. We know that dim( R 3 ) = 3. So, it suffices to check for linear independence. We form a matrix with these vectors as columns and we row reduce it: - 1 2- 3 3- 4 8 1- 3 2 - 1 2- 3 2- 1- 1- 1 - 1 2- 3- 1- 1 2- 1 - 1 2- 3 1 1- 3 - 1 2- 3 1 1 1 , which is an invertible matrix. Therefore, the three vectors are linearly indepen- dent. Problem 3( d ) (Section 1 . 6) Again dim( P 2 ( R )) = 3 and we will only check whether the polynomials are linearly independent or not. Assume a (4 x 2 + 2 x- 1) + b (- 10 x 2- 4 x + 3) + c (- 6 x 2- 5 x- 2) = 0 . Then, (4 a- 10 b- 6 c ) x 2 + (2 a- 4 b- 5 c ) x + (- a + 3 b- 2 c ) = 0 ,or 4 a- 10 b- 6 c 2 a- 4 b- 5 c- a + 3 b- 2 c =...
View Full Document

Page1 / 2

1.6 - Linear Algebra -115 Solutions to Fourth Homework...

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