Unformatted text preview: T HE U NIVERSITY OF S YDNEY P URE M ATHEMATICS Linear Mathematics 2011 Quiz 1a  Solutions
1. The set S = t 1  t R is a subspace of R2 . 0 Which one of the following statements is not true? a) If b) If c) If d) If
x y x y x y x y S then S then S then S then x y 
x y 3 0 S. S. 7 S.
0 1 x y 5x 5y + S. Solution c) x 2. Let X = R2  x 0 . Which one of the following statements is true? y a) X is closed under scalar multiplication, but not closed under addition. b) X is closed under addition and scalar multiplication. c) X is not closed under addition and is not closed under scalar multiplication. d) X is closed under addition, but not closed under scalar multiplication. Solution d) 3. Which one of the following is not a subspace of R3 ? 0 0 a) b) c) d)
0 1 0 0 s 0 0 s t 0 sR  s, t R Solution b) 0 2 0 4. Find the eigenvalues of the matrix 1 1 0. 0 1 1 a) 1, 1, 2 b) 1, 1, 2 c) 1, 1, 2 d) 1, 1, 2 Solution a) Math 2061: Quiz 1a  Solutions S.B. 7/4/2011 Linear Mathematics Quiz 1a  Solutions Page 2 5. Suppose u and v are linearly independ...
View
Full
Document
This note was uploaded on 02/06/2012 for the course MATH 2061 taught by Professor Notsure during the Three '09 term at University of Sydney.
 Three '09
 NOTSURE
 Math

Click to edit the document details