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We are to compute the Singular Value Decomposition (SVD) of the matrix $$ A = \begin{bmatrix} 2 & 1 \\ 1 & 0 \\ 0 & 1 \end{bmatrix} $$ manually. SVD of a matrix $A$ is: $$ A = U \Sigma V^T $$ where: * $U$ is a $3 \times 3$ orthogonal matrix, * $\Sigma$ is a $3 \times 2$ diagonal matrix with singular values, * $V$ is a $2 \times 2$ orthogonal matrix. --- ### Step 1: Compute $A^T A$ $$ A^T = \begin{bmatrix} 2 & 1 & 0 \\ 1 & 0 & 1 \end{bmatrix} $$ $$ A^T A = \begin{bmatrix} 2 & 1 & 0 \\ 1 & 0 & 1 \end{bmatrix} ____ ____ ______ __________ ____ ________ _______ __________ ____ ____.
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