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m20f_prc_midterm_one

# m20f_prc_midterm_one - 3 Determine whether the columns of...

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Practice Midterm I of Math 20F * Jiawang Nie October 19, 2009 Note: You may use a calculator during the exam, but you must show all relevant computational steps. No credit will be given for unsupported answers gotten directly from a calculator. 1. Reduce the following matrix to reduced echelon form: 1 3 5 7 3 5 7 9 5 7 9 1 . Show all the computational steps of how you get the answer. 2. Describe the solution set of the following linear system in parametric vector form x 1 + 3 x 2 - 5 x 3 = 4 x 1 + 4 x 2 - 8 x 3 = 7 - 3 x 1 - 7 x 2 + 9 x 3 = - 6 Show all the computational steps of how you get the answer.
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Unformatted text preview: 3. Determine whether the columns of the following matrix 1 0 3-4-3 0-1 4 5 4 6 is linearly independent or not. Give reasons to justify your answer. 4. Let T : R 3 → R 2 be a linear transformation such that T ( e 1 ) = • 1 3 ‚ ,T ( e 2 ) = • 4-7 ‚ ,T ( e 3 ) = •-5 4 ‚ where e 1 ,e 2 ,e 3 are the columns of the 3 × 3 identity matrix. (a) Is T one-to-one? (b) Is T onto? Give reasons to justify your answer. * The real exam might be totally diﬀerent !!! 1...
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