V issaidtobeaproject… Show more Let V be a finite dimensi

V issaidtobeaproject… Show more Let V be a finite dimensional real vector space. A linear transformation P : V → V issaidtobeaprojection ifP2 = P. (Don’tconfusethiswithorthogonal projections whichareonlydefinedfor inner product spaces. Note that any orthogonal projection is in fact a projection.) (a) For V = R2, give an example of a projection that is not an orthogonal projection.(b) Show that if P is a projection, then the only possible eigenvalues of P are 0 and 1.(c) Show that any projection P is diagonalizable.(d) Conversely, show that if P : V → V is a diagonalizable linear map whose only eigenvalues are 0 or 1, then P must be a projection. • Show less