sample_tt2_1

Sample_tt2_1 - Math 136 Sample Term Test 2 1 NOTES In addition to these questions you should also do questions 4d 5 6 from sample term test 1 1

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: Math 136 Sample Term Test 2 # 1 NOTES: - In addition to these questions you should also do questions 4d, 5, 6 from sample term test 1 # 1. Also, our test covers change of coordinates. 1. Short Answer Problems a) What is the definition of the row space and column space of a matrix A . b) What is the definition of a subspace. c) What is the definition of a basis. d) Let B = 1 2 1 , - 1 2 , 1 1 1 . If [ ~v ] B = 1- 1 1 what is ~v ? e) Let V be a vector space and ~v ∈ V . Prove that (- 1) ~v is the additive inverse of ~v . 2. Let β = { 1 + x 2 , 1 + x + x 2 , 1 + 2 x + 2 x 2 } . a) Show that β is a basis for P 2 . b) Find the β coordinates of the standard basis vectors of P 2 . 3. Determine, with proof, which of the following are subspaces of the given vector space. a) S = { ( x 1 ,x 2 ,x 3 ,x 4 ) ∈ R 4 2 x 1- 5 x 4 = 0 and 3 x 2- 2 x 4 = 0 } of R 4 ....
View Full Document

This note was uploaded on 11/25/2010 for the course MATH 136 taught by Professor All during the Spring '08 term at Waterloo.

Page1 / 2

Sample_tt2_1 - Math 136 Sample Term Test 2 1 NOTES In addition to these questions you should also do questions 4d 5 6 from sample term test 1 1

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