Let A be a non-singular n×n matrix.
a) Show that, in any norm, κ(A) = κ(A⁻¹).
b) By using A⁻¹, show the "companion inequality" to the inequality we proved in class:
∥b∥/∥δb∥ ≤ κ(A)∥δx∥/∥x∥.