MIT18_06S10_exam1_s10_sol

# MIT18_06S10_exam1_s10_sol - 18.06 Quiz 1 March 1 2010...

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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 = + c 1 + c 2 0 1 0 0 0 1 (a) (14 points) What is the 3 by 3 reduced row echelon matrix R and what is d ? Solution: First, since R is in reduced row echelon form, we must have ± T d = 4 0 0 The other two vectors provide special solutions for R , showing that R has rank 1: again, since it is in reduced row echelon form, the bottom two rows must be all 0, and R = ± T the top row is 1 2 5 , i.e. 1 0 2 0 5 0 . 0 0 0 (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 ±nd A and b . Solution:

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MIT18_06S10_exam1_s10_sol - 18.06 Quiz 1 March 1 2010...

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