hw3.6 - Math 43, Fall 2007 B. Dodson Week 9: Monday: Finish...

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Math 43, Fall 2007B. DodsonWeek 9:Monday: Finish Suggested Hw8;start on Hw9 material1.Determinants2.Properties of Dets3.Eigenvalues and Eigenvectors
2We compute det215423951using the(first) row expansion (by minors):det(A) = 2flflflfl2351flflflfl-1flflflfl4391flflflfl+ 5flflflfl4295flflflfl= 2(2-15)-(4-27) + 5(20-18)= 2(-13)-(-23) + 5(2) =-26 + 33 = 7.———–ProblemReduceA=2135301241435253to an upper triagularmatrix and use the reduction to finddet(A).Solution:A-1123301241435253(r1-r2)
-112303711051215071518(r2+ 3r1, r3+ 4r1, r4+ 5r1)-112303711051215011-4(r4-2r2)-1123011-405121503711(r2r4)-1123011-40073500423(r3-5r2, r4-3r2)-1123011-400-1-1100423(r3-2r4)-1123011-400-1-11000-21=U(r

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Term
Spring
Professor
Dodson

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