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Linear AlgebraEasySingular Values & the SVD

Singular Values & the SVD · Easy problem

A matrix has SVD A=UΣVTA = U\Sigma V^{T} with UU, VV orthogonal 3×33\times 3 matrices and Σ=diag⁡(8,5,1)\Sigma = \operatorname{diag}(8, 5, 1). Find the largest value of ∥Ax∥\|Ax\| over all unit vectors x∈R3x \in \mathbb{R}^3.