Need help with number 3 1. Using the matrixFind2. IfVerify that(a) AA' and (AA')-¹.(b) The eigenvalues and eigenvectors of AA'.(c) The eigenvalues and eigenvectors of (AA)-¹A =A = (²₁₁) B=(-²₁) Cc = (3²¹)30(131)-1(a) (A + B) + C = A + (B+C).(b) (AB)C= A(BC).(c) A(B+C) = AB + AC.3. Consider a random vector X'= (X₁, X2, X3) with mean vector ' = (₁, 2, 3) andcovariance matrix Σ. The eigenvalues of E are di 12, A2 = 6, 32 and thecorresponding eigenvectors are1/√3-- ()--(-).=-1/√61/√31/√3(a) Find Σ and trace().(b) Find E and 2-1.(c) Find -1/2.-1/√6e301/√2-1/√2

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Consider a random vector X'= (X₁, X2, X3) with mean vector μ = (1, 2, 3) and covariance matrix E. The eigenvalues of Σ are λ₁ 12, A₂= 6, A3 2 and the corresponding eigenvectors are 1/√3 2/√6 0 -(₁)-(-) (¹²) 1/√√/3 = 1/√√/2 e3 = 1/√√3 (a) Find Σ and trace(). (b) Find E and 2-1. (c) Find E-1/2 = -1/√6 "

Consider a random vector X'= (X₁, X2, X3) with mean vector μ = (1, 2, 3) and covariance matrix E. The eigenvalues of Σ are λ₁ 12, A₂= 6, A3 2 and the corresponding eigenvectors are 1/√3 2/√6 0 -(₁)-(-) (¹²) 1/√√/3 = 1/√√/2 e3 = 1/√√3 (a) Find Σ and trace(). (b) Find E and 2-1. (c) Find E-1/2 = -1/√6 "

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.4: The Singular Value Decomposition

Problem 26EQ

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