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Linear AlgebraEasySingular Values & the SVD

Singular Values & the SVD · Easy problem

A 2×22\times 2 matrix is given by its SVD pieces: A=5 u1v1T+2 u2v2TA = 5\,u_1v_1^{T} + 2\,u_2v_2^{T} with u1=(3/54/5)u_1 = \begin{pmatrix}3/5\\4/5\end{pmatrix}, u2=(−4/53/5)u_2 = \begin{pmatrix}-4/5\\3/5\end{pmatrix}, v1=(10)v_1 = \begin{pmatrix}1\\0\end{pmatrix}, v2=(01)v_2 = \begin{pmatrix}0\\1\end{pmatrix}. Find the entry a21a_{21} (row 2, column 1).