(20pts) Consider the matrixA =−2 11−10 5(a) Determine, by hand, an SVD of A, A = UΣVT. The SVD is not unique,so find the one with the minimum number of minus signs in U and V . List thesingular values σ1 and σ2, and the left and right singular vectors.(b) Find A−1 not directly, but via the SVD. Check your result by typing inv(A)in MATLAB or calculating A−1 by other methods.(c) Find the eigenvalues λ1 and λ2 of A. Verify that detA = λ1λ2 and |detA| =σ1σ2
(20pts) Consider the matrixA =−2 11−10 5(a) Determine, by hand, an SVD of A, A = UΣVT. The SVD is not unique,so find the one with the minimum number of minus signs in U and V . List thesingular values σ1 and σ2, and the left and right singular vectors.(b) Find A−1 not directly, but via the SVD. Check your result by typing inv(A)in MATLAB or calculating A−1 by other methods.(c) Find the eigenvalues λ1 and λ2 of A. Verify that detA = λ1λ2 and |detA| =σ1σ2
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter2: Basic Linear Algebra
Section2.1: Matrices And Vectors
Problem 7P
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(20pts) Consider the matrix
A =
−2 11
−10 5
(a) Determine, by hand, an SVD of A, A = UΣVT. The SVD is not unique,
so find the one with the minimum number of minus signs in U and V . List the
singular values σ1 and σ2, and the left and right singular
(b) Find A−1 not directly, but via the SVD. Check your result by typing inv(A)
in MATLAB or calculating A−1 by other methods.
(c) Find the eigenvalues λ1 and λ2 of A. Verify that detA = λ1λ2 and |detA| =
σ1σ2
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