Linear Algebra Solutions 41

Linear Algebra Solutions 41 - abc Hence ∆ = 2 x y z . uvw...

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Unformatted text preview: abc Hence ∆ = 2 x y z . uvw n2 (n + 1)2 (n + 2)2 2 (n + 2)2 (n + 3)2 (n + 1) (n + 2)2 (n + 3)2 (n + 4)2 3. n2 2n + 1 2n + 3 (n + 1)2 2n + 3 2n + 5 (n + 2)2 2n + 5 2n + 7 C3 → C 3 − C 2 C2 → C 2 − C 1 = n2 2n + 1 2 (n + 1)2 2n + 3 2 (n + 2)2 2n + 5 2 C3 → C 3 − C 2 = n2 2n + 1 2 2n + 1 2 0 2n + 3 2 0 R3 → R3 − R2 R2 → R2 − R1 = = −8. 4. (a) 246 427 327 1014 543 443 −342 721 621 246 1 327 768 0 116 = 100 −588 0 294 = 246 100 327 1014 100 443 −342 100 621 = 100 768 116 −588 294 = 100(−1) 246 1 327 1014 1 443 −342 1 621 = −29400000. (b) 1 2 3 4 −2 1 −4 3 3 −4 −1 2 4 3 −2 −1 = 5 2 11 −10 −10 −10 −5 −14 −17 = −10 5. det A = 5 −3 6 1 0 0 −5 −9 −12 1 0 −2 31 4 5 2 −3 = = 1 2 3 4 0 5 2 11 0 −10 −10 −10 0 −5 −14 −17 = −10 5 2 11 1 1 1 −5 −14 −17 = −10(−1) 10 0 3 1 10 52 7 44 = −3 6 −9 −12 1 10 27 = −13. = 900. ...
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