MATH 1004 Study Guide - Quiz Guide: Eigenvalues And Eigenvectors, Free Variables And Bound Variables, Diagonalizable Matrix
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MATH 1004 Full Course Notes
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If: express the following in the form of and i) Ans: write the polar form of the following complex numbers. Ans: express the following complex numbers in the form of. 1 iz51 iw43 bia wz2243)3). 5()4. (1())4)(5(3. 1(4343. 43514351 iiiiiiiwzii25192517251917 21ziiiiiiiiz247247. 2471162491)4(4. 3. 23(1)43(1122222 iii62524625762524757649247 wz2565025192517251925172 wziwzwz2565025192517251925172 wziwzwziz4 44)0(422 ziz 2sin2cos4242144sin040cos icisz7 z70)7(722 zz )sin(cos77070sin177cos icisz bia )6/(2 ciszmath 1104b tutorial #5 november 23, 2015. Ans: let: for each of the following matrices, find the eigenvalues showing all the steps clearly. Ans: (add 2nd row to the first row, then expand the determinant by the 1st row) iiicisz 321232)6/sin()6/(cos(2)6/(2 4)1(iz 21)1(12211 ziz 43sin43cos2432432121sin2121cos1 icisz 4)0. 1(43sin3cos44. 43sin4. 43cos2441 iiizz 222254245a 222254011222254245)det(ia02224)1()1(2225)1()1(2111 4)2. (4)1(4)2). (5(). 1( 4)2(44)2). (5(). 1( 44842510). 1(2 )10)(1)((1(1011). 1(2 904054447b 904054447)det(ia 5447)9()1(00544)4()1(3313 16)5). (7()9()5(40). 4( )9(16)5)(7)(9()5(16 )5)(7)(9()95(16 )5)(7)(9()7(32 . Ans: (expand the determinant by the 3rd row) So, the eigenvalues are 1,7,13: for the following matrix, either diagonalize it or explain why this is not possible. Since is a triangular matrix, the eigenvalues are 1,1,4: eigenvectors for which implies that is the free variable.
