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Asked: 2024-05-25T08:21:53-04:00 In:

Please answer A and B question 3 a. Find singular value decomposition b. Find a reduced singular value decomposition for the matrix x

Anonymous

a.) Find a singular value decomposition for X = 1-1 11

b.) Find a reduced singular value decomposition for the matrix X in part a.

Please answer A and B question 3 a. Find singular value decomposition b. Find a reduced singular value decomposition for the matrix x




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    1 Answer

    1. Anonymous
      • The SVD factors the matrix X into three components: U, Σ, and V^T.
      • U is a 3×3 orthogonal matrix containing the left singular vectors.
      • Σ is a 3×2 diagonal matrix containing the singular values (4.2426 and a very small value treated as 0).
      • V^T is a 2×2 orthogonal matrix containing the right singular vectors.
      • For the reduced SVD, only the largest singular value (4.2426) and its corresponding vectors in U and V are kept.
      • This provides a rank-1 approximation to the original matrix X.