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MIT18_06S10_exam1_s10

MIT18_06S10_exam1_s10 - 18.06 Quiz 1 March 1 2010 Professor...

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18.06 Quiz 1 March 1, 2010 Professor Strang Your PRINTED name is: 1. Your recitation number or instructor is 2. 3. 4. 1. Forward elimination changes A x = b to a row reduced R x = d : the complete solution is 4 2 5 x = 0 + c 1 1 + c 2 0 0 0 1 (a) (14 points) What is the 3 by 3 reduced row echelon matrix R and what is d ? (b) (10 points) If the process of elimination subtracted 3 times row 1 from row 2 and then 5 times row 1 from row 3, what matrix connects R and d to the original A and b ? Use this matrix to find A and b .
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2. Suppose A is the matrix 0 1 2 2 A = 0 3 8 7 . 0 0 4 2 (a) (16 points) Find all special solutions to Ax = 0 and describe in words the whole nullspace of A . (b) (10 points) Describe the column space of this particular matrix A . “All combinations of the four columns” is not a sufficient answer. (c) (10 points) What is the reduced row echelon form R = rref( B ) when B is the 6 by 8 block matrix A A B = using the same A ? A A
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3. (16 points) Circle the words that correctly complete the following sentence: (a) Suppose a 3 by 5 matrix A has rank r = 3 . Then the equation
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