MIT18_06SCF11_Ses1.9sol

MIT18_06SCF11_Ses1.9sol - Exercises on independence, basis,...

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

View Full Document Right Arrow Icon
± Exercises on independence, basis, and dimension Problem 9.1: (3.5 #2. Introduction to Linear Algebra: Strang) Find the largest possible number of independent vectors among: 1 1 1 = , v 2 = 0 1 0 , v 3 = , 1 0 0 0 v 1 0 1 0 0 0 1 1 0 , v 5 = 1 0 and v 6 = 0 1 v 4 = . 1 1 Solution: Since v 4 = v 2 v 1 , v 5 = v 3 v 1 , and v 6 = v 3 v 2 , the vectors v 4 , v 5 , and v 6 are dependent on the vectors v 1 , v 2 and v 3 . To determine the relationship between the vectors v 1 , v 2 and v 3 we apply row reduction to the matrix [ v 1 v 2 v 3 ] : 1 1 1 1 1 1 1 1 1 1 1 1 −→ −→ 0 1 1 0 0 1 −→ 0 1 1 0 0 1 . 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 / 3

MIT18_06SCF11_Ses1.9sol - Exercises on independence, basis,...

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