Suppose u and v are linearly independent vectors in

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Unformatted text preview: ent vectors in R3 . Which one of the following is a basis for R3 ? a) {u, v, 2u - 3v} b) {u, u + v, u - v} c) {u, v, u v} d) None of the above is a basis for R3 . Solution c) 6. Suppose A is a 3 4 matrix and that the dimension of the null space of A is 1. What is the dimension of the column space of A? a) 1 b) 2 c) 3 d) 4 Solution c) Questions 7 and 8 refer to the matrix A, which has reduced row echelon form J. 1 0 3 2 4 1 0 3 2 4 3 11 , A= 2 1 7 J = 0 1 1 -1 3 . -1 3 0 -5 5 0 0 0 0 0 0 1 2 -1 1 2 -1 1 0 0 0 7. Find a basis for Col(A). 1 0 0 , 1 a) b) c) d) , , , 0 1 0 0 1 3 0 1 3 , , 3 1 0 3 7 0 , , 2 3 -5 2 -1 0 , , 4 3 0 0 1 1 Solution b) 8. Find a basis for Null (A). 2 0 3 3 7 , , 1 a) b) c) d) 0 3 1 , 0 3 1 0 , 0 0 -3 -1 1 0 0 -5 2 -1 , 0 2 -1 0 , 0 0 -2 1 0 1 0 1 4 3 0 4 3 0 0 0 , , -4 -3 0 0 1 Solution d) Math 2061: Quiz 1a -- Solutions Page 2 Linear Mathematics 1 2 0 0 3 0 1 0 6 0 2 0 -1 -2 0 0 Quiz 1a -- Solutions Page 3 9. Let X = a) b) c) d) 1 2 3 4 , , , . What is the dimension of Sp...
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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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