Answer to Question #52681 in Linear Algebra for ravish

Question

a)Find the values of a,b∈C for which the matrix (1. i. 1+i)
( a. 0. b. )
(1−i. 2+i. 1) is Hermitian.(2)b)
Are there values of a∈C for which the matrix (1. 0. 0 )
(0. −1/√2. 1/√2)
(0. 1/√2. a. )
is unitary? Justify your answer.(3)c)Let (x1,x2,x3) and (y1,y2,y3) represent the coordinates with respect to the bases B1={(1,0,0),(0,1,0),(0,0,1)},B2={(1,0,0),(0,1,2),(0,2,1)}.If Q(X)=x21+2x1x2+2x2x3+x22+x23,find the representation of Q in terms of (y1,y2,y3).