Singular Value Decomposition Column Vector

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$Let A: ℝ^n →ℝ^p be of rank r and have singular value decomposition (3.74). Let B1 denote the ball of unit radius in ℝ^n; that is, B1={x ∈ℝ^n,x ≤1} . Use the description of the matrices U, V of Exercise 9 to find the map under A of B1. Distinguish between the cases that p ≥n and p ≤n and also when r<min(n, p). | Numerade$