plugin-hw10 - Assignment 10 Math 417 — Winter 2009 Due...

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Unformatted text preview: Assignment 10 Math 417 — Winter 2009 Due April 10 § 6.1#10. Using the method discussed in class. det 1 1 1 1 2 3 1 3 6 = det 1 1 1 0 1 2 0 2 5 R 2 ← R 2- R 1 R 3 ← R 3- R 1 = det 1 1 1 0 1 2 0 0 1 = 1 ( R 3 ← R 3- 2 R 2 ) § 6.1#20. Using the method discussed in class. det 1 k 1 1 k + 1 k + 2 1 k + 2 2 k + 4 = det 1 1 1 0 1 k + 1 0 2 2 k + 3 R 2 ← R 2- R 1 R 3 ← R 3- R 1 = det 1 1 1 0 1 k + 1 0 0 1 = 1 ( R 3 ← R 3- 2 R 2 ) § 6.1#28. First note that A- λI 3 = 5 7 11 0 3 13 0 0 2 - λ 1 0 0 0 1 0 0 0 1 = 5- λ 7 11 3- λ 13 2- λ is upper triangular for all values of λ . Thus, det( A- λI 3 ) = (5- λ )(3- λ )(2- λ ). This determinant is 0 precisely when λ = 2 , 3 , 5. These are the only values of λ for which A- λI 3 fails to be invertible. 1 § 6.1#42. In this case, cofactor expansion (Theorem 6.2.10) works well: det 1 1 0 1 1 0 2 0 7 0 2 3 4 5 0 0 0 0 3 0 3 4 5 2 6...
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plugin-hw10 - Assignment 10 Math 417 — Winter 2009 Due...

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