Consider the linear system Ax b, where A is invertible Suppose an error b changes b to b ' b b Let x ' be the solution to the new system that is, Ax ' b ' Let x ' x x so that x represents the resulting error in the solution of the system Show that for any compatible matrix norm ...

Consider the linear system Ax = b, where A is invertible. Suppose an error b changes b

Question:

Consider the linear system Ax = b, where A is invertible. Suppose an error Δb changes b to b' = b + Δb. Let x' be the solution to the new system; that is, Ax' = b'. Let x' = x + Δx so that Δx represents the resulting error in the solution of the system. Show that

for any compatible matrix norm.