quiz1-1806-S08-soln

quiz1-1806-S08-soln - 18.06 Professor Strang Quiz 1 March...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 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 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 =...
View Full Document

Page1 / 8

quiz1-1806-S08-soln - 18.06 Professor Strang Quiz 1 March...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online