Construction of minimum norm solution matrix

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Homework Statement


Consider the linear system of equations Ax = b b is in the range of A
Given the SVD of a random matrix A; construct a full rank matrix B for which the solution:
x = B^-1*b
is the minimum norm solution.

Also A is rank deficient by a known value and diagonalizable

Homework Equations





The Attempt at a Solution


I am completely clueless here. I know that due to rank deficiency some eigenvalues of A are zero and this has something to do with the corresponding left and righ singular vectors but I am clueless as to what. I have read through all our notes and can find nothing relating to this problem. Any hint to get me started would be appreciated.
 

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