Calculate the following: (a) Compute the eigenvalues ( lambda_{1} ) and ( lambda_{2} ) of ( R ) and the corresponding eigenvectors ( gamma 1 ) and ( gamma_{2} ) of ( R ) : [ R=left[egin{array}{cc} 0.9 & 1 \ 1 & 0.9 end{array} ight] ] (b) Show that ( lambda_{1}+lambda_{2}=operatorname{tr}(R) ) where the trace of a matrix equals the sum of its diagonal components. (c) Show that ( lambda_{1} imes lambda_{2}=I R I ) where ( I R I ) is the determinant of the matrix.

Calculate the following: (a) Compute the eigenvalues 1 and 2 of R and the corresponding eigenvectors 1 and 2 of R : R=[0.9110.9] (b) Show that 1+2=tr(R) where the trace of a matrix equals the sum of its diagonal components. (c) Show that 12=IRI where IRI is the determinant of the matrix