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Unformatted text preview: 18.06 Professor Strang Quiz 1 March 3, 2008 Grading 1 2 3 4 Your PRINTED name is: Please circle your recitation: 1) M 2 2131 A. Ritter 2085 21192 afr 2) M 2 4149 A. Tievsky 2492 34093 tievsky 3) M 3 2131 A. Ritter 2085 21192 afr 4) M 3 2132 A. Tievsky 2492 34093 tievsky 5) T 11 2132 J. Yin 2333 37826 jbyin 6) T 11 8205 A. Pires 2251 37566 arita 7) T 12 2132 J. Yin 2333 37826 jbyin 8) T 12 8205 A. Pires 2251 37566 arita 9) T 12 26142 P. Buchak 2093 31198 pmb 10) T 1 2132 B. Lehmann 2089 31195 lehmann 11) T 1 26142 P. Buchak 2093 31198 pmb 12) T 1 26168 P. McNamara 2314 41459 petermc 13) T 2 2132 B. Lehmann 2089 21195 lehmann 14) T 2 26168 P. McNamara 2314 41459 petermc 1 (18 pts.) Start with an invertible 3 by 3 matrix A . Construct B by subtracting 4 times row 1 of A from row 3. How do you nd B 1 from A 1 ? You can answer in matrix notation, but you must also answer in words what happens to the columns and rows ? Solution (18 points) We can nd B by multiplying A on the left by an appropriate matrix E 31 (remember, row operations correspond to multiplication on the left, column operations correspond to multiplication on the right). Here, we need E 31 = 1 0 0 1 0 4 0 1 (1) Since B = E 31 A , we know B 1 = ( E 31 A ) 1 = A 1 E 1 31 . Thus, B 1 can be found by doing some column operations on A 1 . What operations speci cally? We know E 1 31 = 1 0 0 0 1 0 4 0 1 (2) (this is the standard pattern for an E matrix). This represents adding 4 times column 3 to column 1. 2 2 (24 pts.) Elimination on A leads to U : Ax = 1 1 1 1 3 3 1 3 7 x 1 x 2 x 3 = 1 leads to Ux = 1 1 1 0 2 2 0 0 4 x 1 x 2 x 3 =...
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 Spring '08
 CHANILLO
 Linear Algebra, Matrices, Column, ax

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