Answer to Question #55010 in Linear Algebra for Ravish

Question

Write true false and give reason

If V is a vector space and T:V→V is a linear operator with det(T)=0,then T is not diagonalisable. The degree of the minimal polynomial of a 3×3 matrix is at most 2. viii) For any 2×2 matrix A,Adj(At)=(Adj(A))t. ix) x) The only matrix which is both symmetric and skew-symmetric is the zero matrix. There is no co-ordinate transformation that transforms the quadratic form x2+y2+z2 to the quadratic form xz+yz.