Matrix Elimination and Substitution?!

I have a numerical method problem which results in a matrix of values, i.e. a 4x4 matrix multiplied by a 4x1 matrix equals a 4x1 matrix. Some of the values in the matrix are already zero but in order to solve it elementary row operations are required to make the matrix a diagonal matrix which can be solved by back substitution. Is this process of elimination and subsititution possible in excel and if so how?

Thanks in advance