matrix = {{X1, Y1, Z1, 0, 0, 0, -u1*X1, -u1*Y1, -u1*Z1, 1, 0},
{0, 0, 0, X1, Y1, Z1, -v1*X1, -v1*Y1, -v1*Z1, 0, 1},
{X2, Y2, Z2, 0, 0, 0, -u2*X2, -u2*Y2, -u2*Z2, 1, 0},
{0, 0, 0, X2, Y2, Z2, -v2*X2, -v2*Y2, -v2*Z2, 0, 1},
{X3, Y3, Z3, 0, 0, 0, -u3*X3, -u3*Y3, -u3*Z3, 1, 0},
{0, 0, 0, X3, Y3, Z3, -v3*X3, -v3*Y3, -v3*Z3, 0, 1},
{X4, Y4, Z4, 0, 0, 0, -u4*X4, -u4*Y4, -u4*Z4, 1, 0},
{0, 0, 0, X4, Y4, Z4, -v4*X4, -v4*Y4, -v4*Z4, 0, 1},
{X5, Y5, Z5, 0, 0, 0, -u5*X5, -u5*Y5, -u5*Z5, 1, 0},
{0, 0, 0, X5, Y5, Z5, -v5*X5, -v5*Y5, -v5*Z5, 0, 1},
{X6, Y6, Z6, 0, 0, 0, -u6*X6, -u6*Y6, -u6*Z6, 1, 0},
{0, 0, 0, X6, Y6, Z6, -v6*X6, -v6*Y6, -v6*Z6, 0, 1}};
inverseMatrix2 = PseudoInverse[matrix]
juzhen_ 2 = Dot[inverseMatrix2, {{u1}, {v1}, {u2}, {v2}, {u3}, {v3}, {u4}, {v4}, {u5}, {v5}, {u6}, {v6}}]
{0, 0, 0, X1, Y1, Z1, -v1*X1, -v1*Y1, -v1*Z1, 0, 1},
{X2, Y2, Z2, 0, 0, 0, -u2*X2, -u2*Y2, -u2*Z2, 1, 0},
{0, 0, 0, X2, Y2, Z2, -v2*X2, -v2*Y2, -v2*Z2, 0, 1},
{X3, Y3, Z3, 0, 0, 0, -u3*X3, -u3*Y3, -u3*Z3, 1, 0},
{0, 0, 0, X3, Y3, Z3, -v3*X3, -v3*Y3, -v3*Z3, 0, 1},
{X4, Y4, Z4, 0, 0, 0, -u4*X4, -u4*Y4, -u4*Z4, 1, 0},
{0, 0, 0, X4, Y4, Z4, -v4*X4, -v4*Y4, -v4*Z4, 0, 1},
{X5, Y5, Z5, 0, 0, 0, -u5*X5, -u5*Y5, -u5*Z5, 1, 0},
{0, 0, 0, X5, Y5, Z5, -v5*X5, -v5*Y5, -v5*Z5, 0, 1},
{X6, Y6, Z6, 0, 0, 0, -u6*X6, -u6*Y6, -u6*Z6, 1, 0},
{0, 0, 0, X6, Y6, Z6, -v6*X6, -v6*Y6, -v6*Z6, 0, 1}};
inverseMatrix2 = PseudoInverse[matrix]
juzhen_ 2 = Dot[inverseMatrix2, {{u1}, {v1}, {u2}, {v2}, {u3}, {v3}, {u4}, {v4}, {u5}, {v5}, {u6}, {v6}}]