-1 3.) Given the matrix A 0 -2 2 1 (a) Find the singular values o; of A. [Hint: first show that the characteristic polynomial of (AT A) is X³ – 13 X² +36 A.] (b) Find the rank 1 matrix A' that is closest to A (with respect to the Frobenius norm). Note: you do NOT necd to find the whole SVD to do this. Find only those parts you need for A'. (c) Find both the Frobenius norm ||A||F and the 2-norm ||A||2 of A. Note: the matrix 2-norm is subordinate to the vector 2-norm.
-1 3.) Given the matrix A 0 -2 2 1 (a) Find the singular values o; of A. [Hint: first show that the characteristic polynomial of (AT A) is X³ – 13 X² +36 A.] (b) Find the rank 1 matrix A' that is closest to A (with respect to the Frobenius norm). Note: you do NOT necd to find the whole SVD to do this. Find only those parts you need for A'. (c) Find both the Frobenius norm ||A||F and the 2-norm ||A||2 of A. Note: the matrix 2-norm is subordinate to the vector 2-norm.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![-1
1
-1
3.) Given the matrix A =
-2
1
1
(a) Find the singular values o; of A.
[Hint: first show that the characteristic polynomial of (AT A) is X³ – 13 X2 + 36 A.]
(b) Find the rank 1 matrix A' that is closest to A (with respect to the Frobenius
norm). Note: you do NOT need to find the whole SVD to do this. Find only
those parts you need for A'.
(c) Find both the Frobenius norm ||A||F and the 2-norm ||A||2 of A.
Note: the matrix 2-norm is subordinate to the vector 2-norm.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8d14a18-18b6-4b9f-91b0-8c8acc9b34e2%2Fad4fde69-9a59-4c82-a013-189376960d6c%2Fi64dg3_processed.png&w=3840&q=75)
Transcribed Image Text:-1
1
-1
3.) Given the matrix A =
-2
1
1
(a) Find the singular values o; of A.
[Hint: first show that the characteristic polynomial of (AT A) is X³ – 13 X2 + 36 A.]
(b) Find the rank 1 matrix A' that is closest to A (with respect to the Frobenius
norm). Note: you do NOT need to find the whole SVD to do this. Find only
those parts you need for A'.
(c) Find both the Frobenius norm ||A||F and the 2-norm ||A||2 of A.
Note: the matrix 2-norm is subordinate to the vector 2-norm.
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