Question

After the forward elimination step of the Gauss elimination method, the coefficient matrix is reduced to ____________

(a) a lower triangular matrix

(b) an upper triangular matrix

(c) a diagonal matrix

(d) a banded matrix

This question was addressed to me in a job interview.

The origin of the question is Numerical Methods in portion Numerical Methods of Computational Fluid Dynamics

Answer 1

The correct answer is (b) an upper triangular matrix

For explanation I would say: After the forward elimination step, the main diagonal elements and the elements above it are non-zeros. All the elements below the main diagonal are zeros. So, we can say that it gives an upper triangular matrix to be solved.