3D skew transformation matrix along one coordinate axis

Question

Is there a way to calculate the skew transformation matrix along one coordinate axis, given the skew angle, as follows

Answer 1

This should work for the most part for skewing an object with a transformation matrix, in particular using glMultMatrix(matrix)

matrix1[] = {
1,  0,  0,  0,
tan(a), 1,  0,  0,
0,  0,  1,  0,
0,  0,  0,  1
};

matrix2[] = {
    1,  0,  0,  0,
    0,  1,  0,  0,
    tan(a), 0,  1,  0,
    0,  0,  0,  1
};

matrix3[] = {
    1,  tan(a), 0,  0,
    0,  1,  0,  0,
    0,  0,  1,  0,
    0,  0,  0,  1
};

matrix4[] = {
    1,  0,  0,  0,
    0,  1,  0,  0,
    0,  tan(a), 1,  0,
    0,  0,  0,  1
};

matrix5[] = {
    1,  0,  tan(a), 0,
    0,  1,  0,  0,
    0,  0,  1,  0,
    0,  0,  0,  1
};

matrix6[] = {
    1,  0,  0,  0,
    0,  1,  tan(a), 0,
    0,  0,  1,  0,
    0,  0,  0,  1
};