1. Show that 2. If is a subordinate matrix norm, prove that Assume the result of Theorem 20.2, and provide an alternate proof of Theorem 20.1. Problems deal with the one-dimensional Poisson...

1.

Show that

2.

If

is a subordinate matrix norm, prove that

Assume the result of Theorem 20.2, and provide an alternate proof of Theorem 20.1.

Problems

deal with the one-dimensional Poisson equation.

In most cases, it is not possible to find an analytical solution, so an approximation technique must be used. Divide the interval into n subintervals of width

, giving
points