hw7s(1) - MATH 4377, ADVANCED LINEAR ALGEBRA, SUMMER 2011,...

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

View Full Document Right Arrow Icon
1. Problem 3 on Page 151. Solution . 0 0 1 0 1 0 1 0 0 - 1 = 0 0 1 0 1 0 1 0 0 , 1 0 0 0 3 0 0 0 1 - 1 = 1 0 0 0 1 / 3 0 0 0 1 , 1 0 0 0 1 0 - 2 0 1 - 1 = 1 0 0 0 1 0 2 0 1 . 2. (i) Find the rank of the matrices in Problem 2 (b), (f) on Page 165. (ii) For the matrices in Problem 2 (b), (f) on Page 165, find a basis for its row space (the vector space spanned by the row vectors of the matrix) and a basis for its cloumn space (the vector space spanned by the column vectors of the matrix), Solution . (i) 2 (b) 1 1 0 2 1 1 1 1 1 -→ 1 1 0 0 - 1 1 0 0 1 -→ 1 0 0 0 1 0 0 0 1 . So its rank is 3 (i.e. the matrix is invertible). 2 (f) 1 2 0 1 1 2 4 1 3 0 3 6 2 5 1 - 4 - 8 1 - 3 1 -→ 1 2 0 1 1 0 0 1 1 - 2 0 0 2 2 - 2 0 0 1 1 5 -→ 1 2 0 1 1 0 0 1 1 - 2 0 0 0 0 2 0 0 0 0 7 -→ 1 2 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 So its rank is 3. 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 5

hw7s(1) - MATH 4377, ADVANCED LINEAR ALGEBRA, SUMMER 2011,...

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