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1. Using the matrix Find 3 1 -- ( ³₁ ₂! 1 ) -1 31 A = (a) AA' and (AA')-¹. (b) The eigenvalues and eigenvectors of AA'. (c) The eigenvalues and eigenvectors of (AA)-¹

1. Using the matrix Find 3 1 -- ( ³₁ ₂! 1 ) -1 31 A = (a) AA' and (AA')-¹. (b) The eigenvalues and eigenvectors of AA'. (c) The eigenvalues and eigenvectors of (AA)-¹

Advanced Engineering Mathematics
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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1. Using the matrix Find 2. If Verify that (a) AA' and (AA')-¹. (b) The eigenvalues and eigenvectors of AA'. (c) The eigenvalues and eigenvectors of (AA)-¹ A = A = (²₁₁) B=(-²₁) Cc = (3²¹) 3 0 (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) and covariance matrix Σ. The eigenvalues of E are di 12, A2 = 6, 32 and the corresponding eigenvectors are 1/√3 -- ()--(-). = -1/√6 1/√3 1/√3 (a) Find Σ and trace(). (b) Find E and 2-1. (c) Find -1/2. -1/√6 e3 0 1/√2 -1/√2
Transcribed Image Text:1. Using the matrix Find 2. If Verify that (a) AA' and (AA')-¹. (b) The eigenvalues and eigenvectors of AA'. (c) The eigenvalues and eigenvectors of (AA)-¹ A = A = (²₁₁) B=(-²₁) Cc = (3²¹) 3 0 (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) and covariance matrix Σ. The eigenvalues of E are di 12, A2 = 6, 32 and the corresponding eigenvectors are 1/√3 -- ()--(-). = -1/√6 1/√3 1/√3 (a) Find Σ and trace(). (b) Find E and 2-1. (c) Find -1/2. -1/√6 e3 0 1/√2 -1/√2
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