hw4-problem2

Hw4-problem2 - O with'linalg BlockDiagonal GramSchmidt JordanBlock LUdecomp QRdecomp Wronskian addcol addrow adj adjoint angle augment backsub band

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Unformatted text preview: O with('linalg'); BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, coldim, colspace, colspan, companion, concat, cond, copyinto, crossprod, curl, definite, delcols, delrows, det, diag, diverge, dotprod, eigenvals, eigenvalues, eigenvectors, eigenvects, entermatrix, equal, exponential, extend, ffgausselim, fibonacci, forwardsub, frobenius, gausselim, gaussjord, geneqns, genmatrix, grad, hadamard, hermite, hessian, hilbert, htranspose, ihermite, indexfunc, innerprod, intbasis, inverse, ismith, issimilar, iszero, jacobian, jordan, kernel, laplacian, leastsqrs, linsolve, matadd, matrix, minor, minpoly, mulcol, mulrow, multiply, norm, normalize, nullspace, orthog, permanent, pivot, potential, randmatrix, randvector, rank, ratform, row, rowdim, rowspace, rowspan, rref, scalarmul, singularvals, smith, stackmatrix, submatrix, subvector, sumbasis, swapcol, swaprow, sylvester, toeplitz, trace, transpose, vandermonde, vecpotent, vectdim, vector, wronskian O A1:=matrix(3,3,[8,-8,-2,4,-3,-2,3,-4,1]); 8 K8 K2 (1) A1 d O eigenvectors(A1); 3 1 1 2, 1, 2 2 4 K3 K2 3 K4 3 2 1 (2) , 1, 1, 2 1 , 3, 1, 211 (3) O T1:=transpose(matrix(3,3,[2,3/2,1,3/2,1,1/2,2,1,1])); 3 2 2 2 T1 d 3 2 1 1 1 2 1 1 (4) O J1:=multiply(inverse(T1),multiply(A1,T1)); 100 J1 d O x0:=vector([1,-1,1]); 020 003 (5) x0 d 1 K1 1 (6) (7) (8) O z0:=multiply(inverse(T1),x0); z0 d K2 K2 4 O x1:=multiply(T1,multiply(exponential(J1*t),z0)); x1 d K et K 3 e2 t C 8 e3 t K et K 2 e2 t C 4 e3 t K et K e2 t C 4 e3 t 4 3 2 (8) (9) O x1:=multiply(exponential(A1*t),x0); x1 d K et K 3 e2 t C 8 e3 t K et K 2 e2 t C 4 e3 t K et K e2 t C 4 e3 t 4 3 2 O A2:=matrix(3,3,[1,0,-4,0,3,0,-2,0,-1]); 1 0 K4 A2 d O eigenvectors(A2); K2 0 1 , 3, 2, 0 3 0 (10) K2 0 K1 010 , K3, 1, 101 (11) O T2:=transpose(matrix(3,3,[-2,0,1,0,1,0,1,0,1])); K2 0 1 T2 d 0 1 10 01 (12) O J2:=multiply(inverse(T2),multiply(A2,T2)); 30 0 J2 d O x0:=vector([1,-1,1]); 03 0 (13) 0 0 K3 x0 d 1 K1 1 (14) (15) (16) (17) O z0:=multiply(inverse(T2),x0); z0 d 0 K1 1 O x2:=multiply(T2,multiply(exponential(J2*t),z0)); 3 3 x2 d eK t K 3 t eK t e O x2:=multiply(exponential(A2*t),x0); 3 3 x2 d eK t K 3 t eK t e O A3:=matrix(3,3,[2,1,1,0,3,1,0,-1,1]); 211 A3 d O eigenvectors(A3); 2, 3, 0 3 1 (18) 0 K1 1 100, 0 1 K1 (19) O T3:=matrix(3,3,[1,0,1,1,0,0,-1,1,0]); 1 01 T3 d 1 00 (20) K1 1 0 O J3:=multiply(inverse(T3),multiply(A3,T3)); 210 J3 d O x0:=vector([1,-1,1]); 020 002 (21) x0 d 1 K1 1 (22) (23) (24) (25) O z0:=multiply(inverse(T3),x0); z0 d K1 0 2 O x3:=multiply(T3,multiply(exponential(J3*t),z0)); x3 d e2 t K 2 t e2 t e O x3:=multiply(exponential(A3*t),x0); x3 d e2 t K 2 t e2 t e O ...
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This note was uploaded on 02/21/2011 for the course ECE 750 taught by Professor Serrani during the Fall '10 term at Ohio State.

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