# quiz1sa - u + v-w =-( u-v + w ) Answer: (a),(b),(d) 5. The...

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January 2010 MATH2061 Linear Algebra Summer School Sample Quiz 1 Each question will be marked out of 2 to give a total out of 10 1. Suppose A = 4 2 0 0 0 - 3 0 0 2 , and b = 8 9 2 . How many solutions does A x = b have? (a) one unique solution (b) inFnitely many solutions (c) exactly two solutions (d) no solutions Answer: (d) 2. Suppose B = p 1 2 3 4 P , and C = p 1 - 2 - 1 1 P ±ind the determinant of BC and the determinant of CB . Answer: 2 2 3. Let U be a vector space with subspaces V and W . Which of the following are always subspaces of U ? (a) the intersection of V and W (b) the union of V and W (c) the complement of V in U Answer: (a) Hint: Think of examples where U = R 2 See other side for remaining questions 1

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4. Let W be a vector space. Let u , v , w W and k R . Which of the items (a) - (e) below are always deFned and true in a vector space? (a) ku W (b) u + v = v + u (c) u.v = v.u (d) k ( u + v ) = ku + kv (e)
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Unformatted text preview: u + v-w =-( u-v + w ) Answer: (a),(b),(d) 5. The Null Space of a 2 2 matrix can be represented geometrically in R 2 as one of the following: (a) a single point at the origin (b) a straight line through the origin (c) the whole plane ( R 2 ) Let A be a 2 2 matrix such that A 2 = A . Which of the items a,b,c above are possible (may be more than one) for the Null Space of a matrix A with A 2 = A ? Answer: (a),(b),(c) or each of the items a,b,c possible for the matrix A , give an example. (Each matrix needs to satisfy the equation A 2 = A .) If no such matrix exists, write none for that item. Answer: (a) (b) (c) p 1 0 0 1 P p 0 0 0 1 P p 0 0 0 0 P 2...
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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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quiz1sa - u + v-w =-( u-v + w ) Answer: (a),(b),(d) 5. The...

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