Question

A DIAGONALIZE K= [ 3/4 53 BY HAND. Now SUPPOSE Ř = is A BIVARIATE Gaussiao VECTOR WITH MEAN ô AND COVARIANCE MATRIX R. WRITE OUT THE JOINT DENSITY OF fa ,xa). IF K=ODOT WHERE o is ORTHOGONAL AND D is DIAGONAL, LET R' = o R © WHERE R' = 537. write out THE Joint DENSITY OF Ē. (6) IF o= cose -sino7 (6) IF 0= sing cose) DETERMINE

2A please

Answer 1

Solution (2A): Given mateix k is, t = 31/4 [sunto 244 let & be the eigen value of k, then det ( K-XI) = 0 to find eigen values, let us first find - K-XI ;

k - r = / 31/7 5/3/7 / الولاده /55 - 3 - آباد کرک | | A k - AE ) - للتو ) (3) = [ ارهاقك = - - - - - - -

=t +34 +36 det [k-dI] =o, ford to be of K . - We know values eigen

- عدد 3 - 3 0 = و = 36 - ۹۸ – ۹۸ -م = ه= (ا - ۹۸ - (ا۔ ۸) د 0 = - (۸) (۸۹) دا values of d are d = 9 or x = 4 So diagonalising mateix k is - diagonal of t = 19