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# quiz1asol - T HE U NIVERSITY OF S YDNEY P URE M ATHEMATICS...

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T HE U NIVERSITY OF S YDNEY P URE M ATHEMATICS Linear Mathematics 2011 Quiz 1a — Solutions 1. The set S = b t p 1 0 P | t R B is a subspace of R 2 . Which one of the following statements is not true? a ) If p x y P S then p x y P - p 3 0 P S . b ) If p x y P S then 7 p x y P S . c ) If p x y P S then p x y P + p 0 1 P S . d ) If p x y P S then p - 5 x - 5 y P S . Solution c) 2. Let X = bp x y P R 2 | x 0 B . Which one of the following statements is true? 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 R 3 ? a ) bp 0 0 0 PB b ) bp 1 0 0 PB c ) bp s 0 0 P | s R B d ) bp s t 0 P | s, t R B Solution b) 4. Find the eigenvalues of the matrix 0 2 0 1 1 0 0 - 1 1 .

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quiz1asol - T HE U NIVERSITY OF S YDNEY P URE M ATHEMATICS...

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