write my assignment 5381

“Justify your answer fully. Show and explain all work for each matrix A.(Ct is transpose of C, C- is inverse of C.)A = -1 8 40 1 -100 0 -1A = -1 -4 00 1 00 10 -1(a) determine whether or not there exists an orthogonal matrix C such that (Ct)AC=V where V is real and diagonal. If so find C and V;proceed to the next matrix. If not, explain why not and proceed to part (b).(b) Determine whether or not there exists an invertible matrix C such that (C-)AC=V where V is real and diagonal. If so, find C and V;proceed to the next matrix. If not, explain why not and proceed to part (c).(c) determine whether or not there exists an invertible matrix C such that (C-)AC=J where J is in Jordan block form. If so, find J.(Note: One does not need to find C.) If not, explain why not and proceed to next matrix.”