Let f : R3 rightarrow R3 with f(x, y, z) = (-x + 3z, 3y + z,2y + z). Write down the matrix [J]e with respect to the canonical basis. Find the matrix [f]B with respect to the basis B = {(1,0,1), (1,1,0), (0,1,1)} of R3. Remember that the columns of [f]B are the coordinates (with respect to B) of the images of the three basis elements. Write down the transition matrix PB from E to B. Use row reduction on the matrix [PB I] to find the inverse P-1 of PB. Find P-1 B [f] e PB (and check it is equal to [/]s). f (1,0,0) = (0,-1,0) = 1(1,0,0)- 1(1,1,0)+ 0(1,1,1), f (1,1,0) = (0,2,2) = -2(1,0,0) + 0(1,1,0) + 2(1,1,1), f (l, 1,1) = (3,3,3) = 0(1,0,0)+0(1,1,0)+ 3(1,1,1). So To find P-1 B. row reduce as follows. Therefore
