I just 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

Let's find |∑| and trace (∑)

3. Consider a random vector X'= (X₁, X2, X3) with mean vector ' = (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 1/√3 (a) Find Σ and trace(). (b) Find E and 2-1. (c) Find E-1/2 - e₁ = 2 e₂ = 2/√√6 -1/√6 -1/√6) e3 = 0 1/√2 -1/√2

3. Consider a random vector X'= (X₁, X2, X3) with mean vector ' = (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 1/√3 (a) Find Σ and trace(). (b) Find E and 2-1. (c) Find E-1/2 - e₁ = 2 e₂ = 2/√√6 -1/√6 -1/√6) e3 = 0 1/√2 -1/√2

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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