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340LExam2B - M340L EXAM 2B SPRING 2008 Dr Schurle Your name...

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M340L EXAM 2B SPRING, 2008 Dr. Schurle Your name: Your UTEID: Show all your work on these pages. Be organized and neat. Your work should be your own; there should be no talking, reading notes, checking laptops, using cellphones, . . . . 1. (8 points) Use a cofactor expansion to compute the following determinant and simplify your result. ± ± ± ± ± ± ± 2 - x - 2 1 0 1 - x 3 2 4 3 - x ± ± ± ± ± ± ±
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YOUR SCORE: /70 2. (8 points) Determine if the set of all polynomials of the form p ( t ) = a + bt +( a + b +1) t 2 is a subspace of P n for an appropriate value of n . Justify your answer. 3. (8 points) (a) If the null space of an 8 × 7 matrix A is 2-dimensional, what is the dimension of the column space of A ? (b) If the dimension of the row space of a 15 × 18 matrix B is 12, what is the dimension of the null space of B ?
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4. (12 points) The matrix A = 1 2 3 - 1 1 2 4 6 - 1 5 3 6 9 - 2 6 7 14 21 - 4 16 is row equivalent to the matrix B = 1 2 3 0 4 0 0 0 1 3 0 0 0 0 0 0 0 0 0 0
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340LExam2B - M340L EXAM 2B SPRING 2008 Dr Schurle Your name...

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