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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...
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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.

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