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