Question

parts a, b, c and d are from example 1.

(a) T21, 12) = (2x - 2.03, -2.6 + 5x2) on V = R2. (b) T(31, 12, 13) = (-11 + 12,5x2, 4.11 - 202 +503) on V = R3. (c) T(21, 12) = (2x + ix, 21 +222) on V = C2 al on V = M2x2(R) (with the Frobenius Inner Product). с (d) T 2. According to Theorems 6.16 and 6.17, for which of the linear operators in Exercise 1 should it be possible to find an ON basis for V consisting of eigenvectors of T?

Answer 1

We find a matrix T with respect to the standard basis in each part of a question.
solution: - Tehod=(2, 2) Q llog -2 (0,1 T(0, 1) = (-2, 5) .) = -211,0) 45 (0,1) is. 2 efficient mabin in -2 5 Tennzang) = (-n, of n a 5h2o uni-222 +503) T(1,0,0) (1, 0, 4) = -1.(110iol to.Corl,0) +4.(0,0,1) (1,5,-2)= 1,(1,0,0) +5. (oil,0) -2.(0,0,1) T(0,1,0) = T10, 0, 1) = (0,0,5) = 0,41,010) torcorp, o) +5. (0,011) Cofficient mation in TE 5 o ५ -25

(c) Т( 11 ) (2, 1) (i, z) T0o,1) 2. (lo) of l.(0,1) eill,ol + 2.10, 1) Cofficient malin . 2 "[.:] = 1:.:] 1 [:)] : [ 0 ] [.:] " [..] - [:)] T[i:] matrin es cofficient O - T= - O 1 O O