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how do we find a vector x so that ||A|| = ||Ax||/||x||(using the infinite norm)

totally no clue on this question..

Q2: Suppose that A is an n×n invertible matrix, and B is an approximation of A's inverse A^-1 such that AB = I + E for some matrix E. Show that the relative error in approximating A^-1 by B is bounded by ||E||(for some arbitrary matrix norm ||· ||).

relative error=(a^-1-B)/A^-1

AB=I+E--------1

AA^-1=I-------2

1/2: B/A^-1=1+E/I=1+E => (A^-1-B)/A^=-E

now I'm stucking...how do I connect -E to norm of E?

am I on the right track?any suggestion? thanks

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