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To find the Singular Value Decomposition (SVD) of the given matrices, we follow these steps: ### (i) Matrix \( A = \begin{bmatrix} -1 & 1 & 1 \\ 1 & 1 & 0 \end{bmatrix} \) 1. Compute \( A^T A \): \[ A^T A = \begin{bmatrix} -1 & 1 \\ 1 & 1 \\ 1 & 0 \end{bmatrix} \begin{bmatrix} -1 & 1 & 1 \\ 1 & 1 & 0 \end{bmatrix} = \begin{bmatrix} 2 & 0 & -1 \\ 0 & 2 & 1 \\ -1 & 1 & 1 \end{bmatrix} \] 2. Find the eigenvalues and eigenvectors of \( A^T A \): - The eigenvalues ___ _____ _________ ________ __________ _______ _______ _____ _______ _________ __________ ______.
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