final-1806-S08

# final-1806-S08 - 18.06 Professor Strang Final Exam Grading...

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18.06 Professor Strang Final Exam May 20, 2008 Grading 1 2 3 4 5 6 7 8 9 10 Your PRINTED name is: Please circle your recitation: 1) M 2 2-131 A. Ritter 2-085 2-1192 afr 2) M 2 4-149 A. Tievsky 2-492 3-4093 tievsky 3) M 3 2-131 A. Ritter 2-085 2-1192 afr 4) M 3 2-132 A. Tievsky 2-492 3-4093 tievsky 5) T 11 2-132 J. Yin 2-333 3-7826 jbyin 6) T 11 8-205 A. Pires 2-251 3-7566 arita 7) T 12 2-132 J. Yin 2-333 3-7826 jbyin 8) T 12 8-205 A. Pires 2-251 3-7566 arita 9) T 12 26-142 P. Buchak 2-093 3-1198 pmb 10) T 1 2-132 B. Lehmann 2-089 3-1195 lehmann 11) T 1 26-142 P. Buchak 2-093 3-1198 pmb 12) T 1 26-168 P. McNamara 2-314 4-1459 petermc 13) T 2 2-132 B. Lehmann 2-089 2-1195 lehmann 14) T 2 26-168 P. McNamara 2-314 4-1459 petermc Thank you for taking 18.06. If you liked it, you might enjoy 18.085 this fall. Have a great summer. GS

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1 (10 pts.) The matrix A and the vector b are A = 1 1 0 2 0 0 1 4 0 0 0 0 b = 3 1 0 (a) The complete solution to Ax = b is x = . (b) A T y = c can be solved for which column vectors c = ( c 1 ,c 2 ,c 3 ,c 4 ) ? (Asking for conditions on the c ’s, not just c in C ( A T ) .) (c) How do those vectors c relate to the special solutions you found in part (a)? 2
2 (8 pts.) (a) Suppose q 1 = (1 , 1 , 1 , 1) / 2 is the ﬁrst column of Q . How could you ﬁnd three more columns q 2 ,q 3 ,q 4 of Q to make an orthonormal basis? (Not necessary to compute them.)

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## This note was uploaded on 08/10/2008 for the course MATH 250 taught by Professor Chanillo during the Spring '08 term at Rutgers.

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final-1806-S08 - 18.06 Professor Strang Final Exam Grading...

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