Condition number of a matrix

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Homework Statement


For a system of equations Ax = b
Let dA be a random perturbation of the matrix A

The error in

Which dA fullfills the equality

norm(A^-1 (da) x) = norm(A^-1) norm(dA) norm(x)

(The SVD of A is known)
(b is a known vector)

Homework Equations





The Attempt at a Solution


I managed to solve a somewhat similar question asking for what b and db fullfills the upper bound for K = norm(A)*norm(b)/norm(x) <= cond(A)

when b = A*V(:,1) and db = U(:,5) <-- clearly rows and columns values corresponding to the smallest singular value of A

However for this particular question I am clueless as to how to form dA to maximise the condition number so it reaches cond(A) = norm(A)*norm(A^-1)
 

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