$$x_1 + x_2 + x_3 = a$$
$$2x_1 - x_2 + 3x_3 = b$$
$$4x_1 + x_2 + 9x_3 = c$$
Now, looking at the solution of this, the author does the following:
The matrix of the coefficients is invertible because $det(E) \ne 0$ (where E is the matrix). Therefore the linear system has only one solution.
Can someone elaborate of the above solution? I do not understand this deduction.