
11. Suppose S: R R2 is the linear transformation with matrix -3 11 [2 -6 2 relative to the bases & and &. Fi...
Let T be the linear transformation from R3 into R2 defined by (1) For the standard ordered bases a and ß for R3 and IR2 respectively, find the associated matrix for T with respect to the bases α and β. (2) Let α = {x1 , X2, X3) and β = {yı, ys), where x1 = (1,0,-1), x2 = - (1,0). Find the associated (1,1,1), хз-(1,0,0), and y,-(0, 1), Уг matrices T]g and T12
5. Let T: P2(R) + RP be the linear transformation that has the matrix …_…………..ນະ 1 2 -1 11 1 1 relative to the bases a = 1+ 21,1+1+12,1+for P2 (R) and B = (1,1),(1,-1) for R2. Find the matrix of T relative to the bases d' = 2+3.r,1+1+12,2+3.+r2 for P2(R) and B' =(3,-1),(1,-1) for R2.
6. Let S : R + R3 be the linear transformation which satisfies |(1,0,0) = (1,0,–3), S(0,1,0) = (0,-1,0) and S(0,0,1) = (1,-1, -2). Give an expression for S(x, y, z). 4 Marks] Let S be the basis (1,0,0), (0,1,0), (0,0,1) for R3 and let T be the basis (0,0,1), (0,1,1), (1,1,1) for R. Compute the change of basis matrix s[1]7. (b) Compute the matrices s[S]s and s[ST. 18 Marks)
-00)0) 2 (AB 22) Let L : R, R2 be a linear transformation. You are given that L 2- 3 (a) Find the matrix A that represents L with respect to the basisu-| | 2-1 1-1 4 1 and the 6 standard basis F1 (b) Find the matrix B that represents IL with respect to the standard basis in both R3 and R2
Find the matrix [T] C-B of the linear transformation T: VW with respect to the bases B and C of V and w, respectively. T: R2 + R3 defined by a + 2b -a b +[:] s={{ ;][-:} c-{{0}{} --13) [) CBT
2. Suppose the linear operator L:R2 + R2 has matrix representation A = (Lee = (_} -). with respect to the basis E = [(1,1), (1, -1)7]. (a) Find B = [L], with respect to the basis F= |(1,0), (2, 1)T] .
DETAILS LARLINALG8 6.R.013. Determine whether the function is a linear transformation. T: R2 – R2, T(x, y) = (x + h. y + k), h + 0 or k + 0 (translation in R2) linear transformation not a linear transformation If it is, find its standard matrix A. (If an answer does not exist, enter DNE in any cell of the matrix.) 11
(1 point) Let S be a linear transformation from R2 to R2 with associated matrix A= Let T be a linear transformation from IR2 to R2 3 1 ]' Determine the matrix C of the composition ToS
Let L : R2 → R3 be a linear transformation such that L 1 1 = 1 2
3 and L 1 2 = 2 1 3 . Find L 2 1 Find the standard matrix
representing L. Find the dimensions of the kernel and the range of
L and their bases.
12. Let L : R² + RP be a linear transformation such that L | (3) - -(5)-(1) Find I (*) Find the standard matrix representing L. Find...
(3) Suppose T is a linear transformation, T: R2 R3 and Find the matrix C of T such that T(T) = Cő for all 7.