[a] Let I E R\" he distributed as :e m MVNHLI}. We shut-med in class that if A is sy'rnrnetIie and ideml'itttutentr then 11A: is distributed as Iii- Whf k = rka]- FnI this prnhlern, shew the tit-inverse, is, if A is symmetric and ITAI is 1*: then A is ideuipnteut and rka} = k. Hint: by the spmtral deennip-nsitien thmrem :TA: = ices? i=1 1Where the 31- nre independent Nfl], 1} randnni variables and the d.- are the eigenvalues nf A: i_e_1, :TA: is a weighted sum nf independent. 1%. thw that the :1thnt t; = :TA: is then TREES) = 11;,[1 Jetty\"? New the mat fer xi is [l 23}'HE_ What. dues this seq.-r ahnut the enlleetinn {di} 1"