> restart;
> with(linalg);
Warning, the protected names norm and trace have been redefined and unprotected


  [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]

> A:=matrix(6,6,[-1 ,      0      , cos(alpha) ,  1 ,  1 ,  0 ,
>                 0 ,      1      , sin(alpha) ,  0 ,  0 , -1 ,
>                 0 ,      1      ,     0      , -1 ,  0 ,  2 ,
>                 0 , -cos(alpha) ,     0      , -1 , -1 ,  0 ,
>                 0 ,  sin(alpha) ,     1      ,  0 ,  0 ,  1 ,
>                 0 ,      0      ,    -1      ,  1 ,  0 ,  2 ]);  

            [-1         0         cos(alpha)     1     1     0]
            [                                                 ]
            [ 0         1         sin(alpha)     0     0    -1]
            [                                                 ]
            [ 0         1             0         -1     0     2]
       A := [                                                 ]
            [ 0    -cos(alpha)        0         -1    -1     0]
            [                                                 ]
            [ 0    sin(alpha)         1          0     0     1]
            [                                                 ]
            [ 0         0             -1         1     0     2]

> b:=matrix(6,1,[0 , F , 0 , 0 , 2*F , 0]);

                                   [ 0 ]
                                   [   ]
                                   [ F ]
                                   [   ]
                                   [ 0 ]
                              b := [   ]
                                   [ 0 ]
                                   [   ]
                                   [2 F]
                                   [   ]
                                   [ 0 ]

> linsolve(A,b);

        [   2 cos(alpha) F  ]
        [- -----------------]
        [  -3 + 2 sin(alpha)]

        [           F (-7 + 8 sin(alpha))        ]
        [1/2 ------------------------------------]
        [    (sin(alpha) + 1) (-3 + 2 sin(alpha))]

        [           F (-11 + 4 sin(alpha))       ]
        [1/2 ------------------------------------]
        [    (sin(alpha) + 1) (-3 + 2 sin(alpha))]

        [          F       ]
        [3/2 --------------]
        [    sin(alpha) + 1]

        [-1/2 F

        (-7 cos(alpha) + 8 cos(alpha) sin(alpha) - 9 + 6 sin(alpha))/

        ((sin(alpha) + 1) (-3 + 2 sin(alpha)))]

        [             F        ]
        [-1/2 -----------------]
        [     -3 + 2 sin(alpha)]

> alpha:=Pi/6;

                                      Pi
                            alpha := ----
                                      6

>