homework2_solutions - MATH 211(Siefken Homework#2 John Q Student Due Question#1 3(a Find the inverse of A = 6 1 1 3 1 2 5 by GaussJordan elimination 3

homework2_solutions - MATH 211(Siefken Homework#2 John Q...

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John Q. Student MATH 211 (Siefken): Homework #2 Due May 26, 2011 Question #1(a) Find the inverse ofA=312635113by Gauss–Jordan elimination.To findA-1we apply Gauss-Jordan elimination to [ (b) Solve the following system of equations3x1y2z=-16x3y5z=2x+y+3z=3. Question #2For each of the following statements, if they are true,prove them, otherwise provide a specificcounterexample.(a) IfAandBare both 2×2 matrices which are not diagonal (and so neither is the zero matrix), thenAB=BAimpliesA=B.Question #2 continued on next page. . . Page 1 of 6
John Q. Student MATH 211 (Siefken): Homework #2 Due May 26, 2011 Consider A = 3 1 1 3 and B = 3 - 1 - 1 3 . We have AB = BA = 8 0 0 8 , but A 6 = B . (b) If c R with c 6 - 1 . 6

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