# Triangular Matrix

A. Now consider the product P = ST R S, where S is an upper triangular matrix having 0 everywhere except 1 on the main diagonal and ?1 on the first super diagonal. Write the exact form of P.

B. A new algorithm is now proposed to solve the linear system Rx = b.

It is in four steps:
Step A. Let x = Sy to get R Sy = b.
Step B. Multiply both sides of R Sy = b by ST to write ST R Sy = STb = c or Py = c.
Step C. Solve Py = c to obtain y.
Step D. Compute x as x = Sy.

Show the computations performed at each step when the data vector b = 1 1 1 ? 1T.

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