Given that E is an ordered basis for R^2, and that S is the transition matrix from E toF=[v1,v2], determine the vectors v1 and v2 E= (1), (1)      S= (1), (3)       (1), (-1)          (-1), (2)

Find the matrix A' for T relative to the basis B'. T: R² A' = R², T(x, y) = (x + y, 3y), B' = {(-4, 1), (1, -1)}

C: Let T be the linear operator associated in the standard basis B of F2 with the matrix 2 - [44] - 1 Let B' be the basis ((2, -1), (2, 1)) M = b) Using eachof these three matrices find the dimension of the range of T (you must check that the dimension is the same with all the matrices)

Find the coordinate matrix of x in R" relative to the basis B. B' = {(8, 11, 0), (7, 0, 10), (1, 4, 6)), x = (-4, 19, -8) [x] = 000 11 It 7

Find the transition matrix from the basis B = {(1,2,3) (1,0,1)(1,2,1)} to B' = {(1,1,0)(0,1,1)(1,1,1)}.