Question

HW13.3. Calculate a matrix using its SVD A 2 × 3 matrix A satisfies the following: A^T A has the eigenvalues 8, 4, 0, with w_1 = 1/?3 [1; 1; 1] an eigenvector for eigenvalue 8 and w_2 = [-1; 1; 0] an eigenvector for eigenvalue 4. If ?8 [0.45; -0.89] = Aw_1 ? Col(A), find a possible matrix A. A = [[1, -1, 0], [2, 2, 2]]

          HW13.3. Calculate a matrix using its SVD

A 2 × 3 matrix A satisfies the following: A^T A has the eigenvalues 8, 4, 0, with w_1 = 1/?3 [1; 1; 1] an eigenvector for eigenvalue 8 and w_2 = [-1; 1; 0] an eigenvector for eigenvalue 4. If ?8 [0.45; -0.89] = Aw_1 ? Col(A), find a possible matrix A.
A = [[1, -1, 0], [2, 2, 2]]

HW13.3. Calculate a matrix using its SVD

A 2 × 3 matrix A satisfies the following: A^T A has the eigenvalues 8, 4, 0, with w1 = 1/?3 [1; 1; 1] an eigenvector for eigenvalue 8 and w2 = [-1; 1; 0] an eigenvector for eigenvalue 4. If ?8 [0.45; -0.89] = Aw1 ? Col(A), find a possible matrix A.
A = [[1, -1, 0], [2, 2, 2]]

Added by Stephanie G.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Brent Burkett

Step 1

We know that the singular value decomposition (SVD) of a matrix A is given by A = UΣV^T, where U and V are orthogonal matrices and Σ is a diagonal matrix with singular values on the diagonal. Show more…

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Calculate matrix using its SVD A 2 × 3 matrix A satisfies the following: A^T A has the eigenvalues 8, 4, 0, with w1 as an eigenvector for eigenvalue 8 and w2 as an eigenvector for eigenvalue 4. If √8 [0.45; -0.89] = Aw1 ∈ Col(A), find a possible matrix A. A =