Question 21 , 22 , 24 , 25.

Question 21 Let TA be the linear operator corresponding to multiplication by the matrix A, that is, TA (x) = Ax. Which of the following are True? O T (el) = e1, where Th = TAOTAO TA O TA O TA. O TA is not one-to-one O TA (e2) = (0, 8, 2) If T(x) = 0 then x = 0 O T (-6,9,2) = (1, 1, 1) T_A^(-1}(-6,9,2)=(1,1,1) Question 22 Use matrix inversion and your answer above to solve the system -11 Ax = 21 2:2Question 24 Let V = R4 with Euclidean Inner Product, and let W = span{v1, v2, V3} wherev1 = (1, -1, 3, 2), v2 = (2, -2, 7, 4), v3 = (-3,3, -7, -6). . (3 marks) State a basis for W. . (3 marks) State a basis for WI. NOTE: only the final answers will be graded. BIUA . A . LEE 3 1 I XX BE - & V G 1 1 12 pt Paragraph 0 words D Question 25 2.pts (Cryptography) Suppose that a Hill 2-cipher uses the matrix A = > >|to encrypt messages. Find the matrix A l used to decrypt messages. Your matrix should have as entries integers from 0 to 25. Table of inverses : 5 7 11 15 17 19 21 23 25 21 15 3 19 7 23 11 5 17 25 When answering you'll need to access the math editor (click on \\ above and click on "switch view to advanced"). Here is a template you can copy and paste for an answer that is a matrix with 2 rows, 2 columns