Back Substitution

In today’s lab we will write a program to solve an upper triangular matrix using back substitution. The basic algorithm is the one that you have seen in class. The pseudocode can be described as:

for j = n to 1                 //loop over columns
    if u_jj = 0 then stop      //stop if matrix is singular
    x_j = b_j/u_jj             //compute component solution
    for i = 1 to j-1         //
        b_i = b_i-u_ij*x_j     //update RHS
    end
end

Try the program on the following upper triangular system

| 4   -1    2   3  || x_1 |     | 20 |
| 0   -2    7   -4 || x_2 |     | -7 |
| 0    0    6   5  || x_3 |  =  |  4 |
| 0    0    0   3  || x_4 |     |  6 |