> with(linalg);
Warning, new definition for norm
Warning, new definition for trace

[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, stack, submatrix,

    subvector, sumbasis, swapcol, swaprow, sylvester, toeplitz, trace,

    transpose, vandermonde, vecpotent, vectdim, vector, wronskian]

> A := transpose(matrix(3,4, [1,1,1,1, 15, 20, 30, 50,
> 15*ln(15), 20*ln(20), 30*ln(30), 50*ln(50)])); 

                          [1    15    15 ln(15)]
                          [                    ]
                          [1    20    20 ln(20)]
                     A := [                    ]
                          [1    30    30 ln(30)]
                          [                    ]
                          [1    50    50 ln(50)]

> b := vector([44, 62, 115, 224]);

                       b := [44, 62, 115, 224]

> read
> `/afs/unity.ncsu.edu/project/www/ncsu/Project25/MA305/Maple/initlib.mp
> l`
> ;

libname :=

    /afs/unity.ncsu.edu/project/www/ncsu/Project25/MA305/Maple,

    /afs/bp.ncsu.edu/dist/maple54/update,

    /afs/bp.ncsu.edu/dist/maple54/lib


table([

    myinverse = readlib(refpkg/myinverse)

    mysolve = readlib(refpkg/mysolve)

    mydet = readlib(refpkg/mydet)

    xref = readlib(refpkg/xref)

    E_II = readlib(refpkg/E_II)

    ref = readlib(refpkg/ref)

    E_III = readlib(refpkg/E_III)

    E_I = readlib(refpkg/E_I)

    ])


table([

    gram_schmidt = readlib(lsqpkg/gram_schmidt)

    ])

> with(lsqpkg);

                            [gram_schmidt]

> ?gram_schmidt
> Q := gram_schmidt(A, 'R');
> 

Q :=

    [            168          192          156          180       ]
    [1 , -55/4 , --- ln(15) - --- ln(20) - --- ln(30) + --- ln(50)]
    [            23           23           23           23        ]

    [            296          144          162          10       ]
    [1 , -35/4 , --- ln(20) - --- ln(15) - --- ln(30) + -- ln(50)]
    [            23           23           23           23       ]

    [          516          78          108          330       ]
    [1 , 5/4 , --- ln(30) - -- ln(15) - --- ln(20) - --- ln(50)]
    [          23           23          23           23        ]

    [           140          54                        198       ]
    [1 , 85/4 , --- ln(50) + -- ln(15) + 4/23 ln(20) - --- ln(30)]
    [           23           23                        23        ]

> print(R);

    [1 , 115/4 , 15/4 ln(15) + 5 ln(20) + 15/2 ln(30) + 25/2 ln(50)]

    [          33           28                          34       ]
    [0 , 1 , - --- ln(15) - --- ln(20) + 6/115 ln(30) + -- ln(50)]
    [          115          115                         23       ]

    [0 , 0 , 1]

> Diag := evalm(transpose(Q) &* Q);

Diag :=

    [4 , 0 , 0]

    [0 , 2875/4 , 0]

    [        /168          192          156          180       \2
    [0 , 0 , |--- ln(15) - --- ln(20) - --- ln(30) + --- ln(50)|
    [        \23           23           23           23        /

       /296          144          162          10       \2
     + |--- ln(20) - --- ln(15) - --- ln(30) + -- ln(50)|
       \23           23           23           23       /

       /516          78          108          330       \2
     + |--- ln(30) - -- ln(15) - --- ln(20) - --- ln(50)|
       \23           23          23           23        /

       /140          54                        198       \2]
     + |--- ln(50) + -- ln(15) + 4/23 ln(20) - --- ln(30)| ]
       \23           23                        23        / ]

> b2 := evalm(transpose(Q) &* b);

      [
b2 := [445, 15025/4,
      [

    1590          1620          1920          1950       ]
    ---- ln(15) - ---- ln(20) - ---- ln(30) + ---- ln(50)]
     23            23            23            23        ]

> b3 := evalm(inverse(Diag) &* b2);

      [       601  23 /
b3 := [445/4, ---, -- |
      [       115  40 \

    1590          1620          1920          1950       \   /
    ---- ln(15) - ---- ln(20) - ---- ln(30) + ---- ln(50)|  /  (
     23            23            23            23        / /

             2
    63 ln(15)  - 144 ln(15) ln(20) - 117 ln(15) ln(30)

                                     2
     + 135 ln(15) ln(50) + 148 ln(20)  - 162 ln(20) ln(30)

                                    2
     + 10 ln(20) ln(50) + 387 ln(30)  - 495 ln(30) ln(50)

                 2 ]
     + 175 ln(50) )]
                   ]

> b4 := evalm(inverse(R) &* b3);

      [
      [
      [      23 (-12 ln(15) - 12 ln(20) - 6 ln(30) + 30 ln(50)) %1
b4 := [-39 + -- --------------------------------------------------,
      [      40                         %2

             /33           28                          34       \
             |--- ln(15) + --- ln(20) - 6/115 ln(30) - -- ln(50)| %1
    601   23 \115          115                         23       /
    --- + -- -------------------------------------------------------,
    115   40                           %2

           ]
           ]
    23  %1 ]
    -- ----]
    40  %2 ]

      1590          1620          1920          1950
%1 := ---- ln(15) - ---- ln(20) - ---- ln(30) + ---- ln(50)
       23            23            23            23

               2
%2 := 63 ln(15)  - 144 ln(15) ln(20) - 117 ln(15) ln(30)

                                     2
     + 135 ln(15) ln(50) + 148 ln(20)  - 162 ln(20) ln(30)

                                    2
     + 10 ln(20) ln(50) + 387 ln(30)  - 495 ln(30) ln(50)

                 2
     + 175 ln(50)

> evalf(evalm(b4));

                [.56617708, -.955521423, 1.387891671]

> 
>