Consider the matrix A = [-120 5]. (a) Determine the SVD of A by hand. (b) List the singular values, left singular vectors, and right singular vectors of A. Draw a careful, labeled picture of the unit circle in R² and its image under A, together with the singular vectors, with the coordinates of their vertices marked. (c) What are the 1-, 2-, -, and Frobenius norms of A? (d) Use the SVD to find A-¹. (You must show your work and how you used SVD.)
Consider the matrix A = [-120 5]. (a) Determine the SVD of A by hand. (b) List the singular values, left singular vectors, and right singular vectors of A. Draw a careful, labeled picture of the unit circle in R² and its image under A, together with the singular vectors, with the coordinates of their vertices marked. (c) What are the 1-, 2-, -, and Frobenius norms of A? (d) Use the SVD to find A-¹. (You must show your work and how you used SVD.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Dd.58.
Transcribed Image Text:Consider the matrix
A =
-2 11
-10 5
(a) Determine the SVD of A by hand.
(b) List the singular values, left singular vectors, and right singular vectors of A. Draw a careful,
labeled picture of the unit circle in R² and its image under A, together with the singular
vectors, with the coordinates of their vertices marked.
(c) What are the 1-, 2-, -, and Frobenius norms of A?
(d) Use the SVD to find A-¹. (You must show your work and how you used SVD.)
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