1. Consider the following matrix:The SVD of this matrix isU=Σ =v=A =1.0723 2.1690 2.7877 1.13073.9083 4.7857 6.2692 1.83437.0398 8.0931 8.8831 0.0720L0.0207 – 1.9516 0.9392 4.0374]0.1753 0.7666 0.5781-0.2179-0.52630.2606 0.3434 -0.7329-0.8218 0.2006 -0.4278 0.31840.0113 0.9280 -0.3338 0.165416.896400004.91970(a) What is the rank of A?(b) By A, construct a matrix of rank 2.0001.0101000[-0.4780 0.0379-0.8460 -0.2334]-0.5720 0.3673 0.4902 - 0.5456-0.6627 -0.2464 0.1743 0.6854-0.0725 -0.8961 0.1172 0.4220](c) Let B = o₁u₁v₁, where σ₁ is the (1,1) entry of the matrix Σ, i.e., Σ(1,1)= 0₁, the vectors U₁and v₁ are the first column of the matrices u and v, respectively.Without directly computing, find the value of ||A - B||F?

Answered: Image /qna-images/answer/f811293c-007e-4f89-8659-1f10db3d27a4.jpg

1. Consider the following matrix: The SVD of this matrix is U = Σ = V = A = 1.0723 2.1690 2.7877 1.1307 3.9083 4.7857 6.2692 1.8343 7.0398 8.0931 8.8831 0.0720 L0.0207 – 1.9516 0.9392 4.0374J -0.2179 - 0.1753 0.7666 0.5781 -0.5263 0.2606 0.3434 -0.7329 -0.8218 0.2006 - 0.4278 0.3184 0.0113 0.9280 0.3338 0.1654 16.8964 0 0 0 0 4.9197 0 0 0 0 1.0101 0 Without directly computing, find the value of ||A - B||F? 0 0 0 0 [-0.4780 0.0379-0.8460 - 0.23341 -0.5720 0.3673 0.4902 - 0.5456 -0.6627 -0.2464 0.1743 0.6854 -0.0725 - 0.8961 0.1172 -0.4220] (a) What is the rank of A? (b) By A, construct a matrix of rank 2. (c) Let Bo₁u₁v₁, where σ₁ is the (1,1) entry of the matrix Σ, i.e., Σ(1,1)= 0₁, the vectors ₁ and v₁ are the first column of the matrices u and v, respectively.

1. Consider the following matrix: The SVD of this matrix is U = Σ = V = A = 1.0723 2.1690 2.7877 1.1307 3.9083 4.7857 6.2692 1.8343 7.0398 8.0931 8.8831 0.0720 L0.0207 – 1.9516 0.9392 4.0374J -0.2179 - 0.1753 0.7666 0.5781 -0.5263 0.2606 0.3434 -0.7329 -0.8218 0.2006 - 0.4278 0.3184 0.0113 0.9280 0.3338 0.1654 16.8964 0 0 0 0 4.9197 0 0 0 0 1.0101 0 Without directly computing, find the value of ||A - B||F? 0 0 0 0 [-0.4780 0.0379-0.8460 - 0.23341 -0.5720 0.3673 0.4902 - 0.5456 -0.6627 -0.2464 0.1743 0.6854 -0.0725 - 0.8961 0.1172 -0.4220] (a) What is the rank of A? (b) By A, construct a matrix of rank 2. (c) Let Bo₁u₁v₁, where σ₁ is the (1,1) entry of the matrix Σ, i.e., Σ(1,1)= 0₁, the vectors ₁ and v₁ are the first column of the matrices u and v, respectively.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 41EQ

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