RQ3 -       =       3 7...

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UCSC MATH 21 FALL 2007 Review Questions 3 1. Consider the matrix A = 1 1 1 1 6 1 2 3 4 2 15 0 1 2 3 3 11 3 2 1 0 2 9 4 3 2 1 1 13 1 . a. Find the reduced-row-echelon form of A . Suggestion: keep track of the row operations that you use. b. Find a basis for the null space of A . c. Find a basis for the column space of A . d. Find a basis for the row-space of A . 2. Use your answer to 1b. (and the record you kept in 1a. ) to describe the set of solutions to the system 1 1 1 1 6 1 2 3 4 2 15 0 1 2 3 3 11 3 2 1 0 2 9 4 3 2 1 1 13 1 x 1 x 2 x 3 x 4 x 5 x 6
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Unformatted text preview:       =       3 7 6 5 6       . 3. Let W ⊂ R 5 be the subspace spanned by the vectors w 1 =       1 2 1-3       , w 2 =       2 1-1 3       and w 3 =       2 3-2 1 1       . Find a basis for W ⊥ . 4. Problems 37, 39, 41, 43, 45 and 47 on page 122. 5. Problem 31 on page 134 and problem 53 on page 135. 1...
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This note was uploaded on 03/16/2010 for the course ECON 11 taught by Professor Yk during the Spring '10 term at University of California, Santa Cruz.

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