Define T : P2 rightarrow P2 by T(a + bx + cx2) = (b + c) + (a + c)x + (a + b)x2. Show that T is diagonalizable by exhibiting a basis of P2 consisting of eigenvectors. (You need not verify that T is linear.)
Show transcribed image textDefine T : P2 rightarrow P2 by T(a + bx + cx2) = (b + c) + (a + c)x + (a + b)x2. Show that T is diagonalizable by exhibiting a basis of P2 consisting of eigenvectors. (You need not verify that T is linear.)