Consider the n × n lower-triangular system Ax = b, where A = (ai j ) and ai j = 0 for i...

Consider the n × n lower-triangular system Ax = b, where A = (a_{i j} ) and a_{i j} = 0 for i < j .

a a. Write an algorithm (in mathematical terms) for solving for x by forward substitution.

b. Write

procedure Forward_ Sub(n, (a_i ), (b_i ), (x_i ))

which uses this algorithm.

c. Determine the number of divisions, multiplications, and additions (or subtractions) in using this algorithm to solve for x.

d. Should Gaussian elimination with partial pivoting be used to solve such a system?