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oldexam2

# oldexam2 - A 2(e Find the general solution to A x = b where...

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Math 290 - Exam 2 - November 2, 2006 Name: Directions: Do all your work on these pages, using the backs if necessary. There are 5 problems, and the point totals are indicated. 1. Definitions (5 pts each) : (a) The vectors { v 1 , . . . , v k } are linearly dependent if (b) The span of { v 1 , . . . , v k } is (c) The rank of the matrix A is (d) The vectors { v 1 , . . . , v k } form a basis for V if (e) The null space of the matrix A is 2. (20 pts) Can 1 1 0 be written as a linear combination of 2 2 1 and 1 0 - 1 ? (You must show that it can or cannot - a simple “yes” or “no” is not worth anything.) 1

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3. (25 pts) Let A = 3 2 1 1 10 1 - 1 4 0 (a) Find a basis for the row space of A . (b) What is the rank of A ? (c) Find a basis for the column space of A . (d) Find a basis for the null space of
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Unformatted text preview: A . 2 (e) Find the general solution to A x = b , where b = 1 1 . 4. True or False? (5 pts each) - no reason need be given (a) The polynomials { t + 1 , t-1 } are linearly independent in P 3 (b) The range of A m × n is the same as the span of the columns of A . (c) Any three vectors in R 2 are linearly dependent. (d) The set of all solutions to A x = b ( b 6 = ) is a subspace. 5. (10 pts) (a) Suppose A is a 3 × 5 matrix, and suppose that for some b , the equation A x = b has a solution x p . Is it possible that x p is the only solution? Give a reason for your answer. (b) Same question, except that this time, A is 5 × 3. 3...
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oldexam2 - A 2(e Find the general solution to A x = b where...

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