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
Unformatted text preview: Math 136 Sample Term Test 2 # 2 NOTES:  In addition to these questions you should also do questions 7, 10 b from sample term test 1 # 2. Also, our test covers change of coordinates. 1. Short Answer Problems a) Let S = { ~v 1 ,...,~v n } be a nonempty subset of a vector space V . Define the statement S is linearly independent. b) Write the definition of a subspace S of a vector space V . c) Write the definition of the dimension of a vector space V . d) Prove that 0 ~x = ~ 0 for any ~x V . e) Is it true that if a set S with more than one vector is linearly dependent, then every vector ~v S can be written as a linear combination of the other vectors. Justify your answer. 2. Let B = { x 2 4 x + 4 ,x 2 , 1 } . a) Show that Span B = P 2 . b) Let ~w = x 2 + x + 1. Find the [ ~w ] B . 3. Determine, with proof, which of the following are subspaces of the given vector space. a) S = { ax 2 + bx + c  b 2 4 ac 6 = 0 } of P 2 ....
View
Full
Document
 Spring '08
 All
 Linear Algebra, Algebra, Addition

Click to edit the document details