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final-1806-F05

final-1806-F05 - 18.06 Professor Strang Final Exam Grading...

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18.06 Professor Strang Final Exam December 19, 2005 Grading 1 2 3 4 5 6 7 8 Your PRINTED name is: Please circle your recitation: 1) M 2 2-131 P. Lee 2-087 2-1193 lee 2) M 2 2-132 T. Lawson 4-182 8-6895 tlawson 4) T 10 2-132 P-O. Persson 2-363A 3-4989 persson 5) T 11 2-131 P-O. Persson 2-363A 3-4989 persson 6) T 11 2-132 P. Pylyavskyy 2-333 3-7826 pasha 7) T 12 2-132 T. Lawson 4-182 8-6895 tlawson 8) T 12 2-131 P. Pylyavskyy 2-333 3-7826 pasha 9) T 1 2-132 A. Chan 2-588 3-4110 alicec 10) T 1 2-131 D. Chebikin 2-333 3-7826 chebikin 11) T 2 2-132 A. Chan 2-588 3-4110 alicec 12) T 3 2-132 T. Lawson 4-182 8-6895 tlawson

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1 (12 pts.) This question is about the matrix A = I + E where E is the all-ones matrix ones (4 , 4): A = 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 = I + 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 . (a) By elimination find the pivots of A . (b) Factor A into LDL T (if that is possible). (c) The inverse matrix has the form A - 1 = I + cE . Figure out E 2 and then choose the number c so that AA - 1 = I .
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