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Chapter 8, Section 8.1, Question 20 Consider the basis S = {vj, v2} for R2, where v, = (- 2, 1) and v2 = (1, 3), and let 7:82 - R3 be the linear transformation such that T(v1 ) = (- 1, 4, 0) and T(v2) = (0, - 5, 9) Find a formula for 7(x1, x2), and use that formula to find 7(4, - 5). Give exact answers in the form of a fraction. T ( 4, -5) = EditChapter 5, Section 5.2, Supplementary Question 02 Find the geometric and algebraic multiplicity of each eigenvalue, and determine whether A is diagonalizable. If so, find a matrix P that diagonalizes A, and determine PAP (Notice that the order of the eigenvalues and corresponding eigenvectors can be different from yours and that the eigenvectors are defined accurately to the factor (sign).) 0 O N 0 0 -2 20 -20 A = 0 0 0 0 3 O A = -2. Algebraic multiplicity = Geometric multiplicity = 1. A = 3. Algebraic multiplicity = 2, Geometric multiplicity = 1. A is not diagonalizable. O A = -2. Algebraic multiplicity = Geometric multiplicity = 2. A = 3. Algebraic multiplicity = Geometric multiplicity = 2. 0 O 2 0 0 0 4 P-AP = 0 N P = T -4 0 0 0 1 0 0 3 WOO 0 O 1 0 0 0O A = 2. Algebraic multiplicity = Geometric multiplicity = 2. A = 3. Algebraic multiplicity = Geometric multiplicity = 2. 1111111 zoo P2111144, P-1AP2o2 o no 01 DID3 oo1o one Q A = 2. Algebraic multiplicity = 2, Geometric multiplicity = l. A = 3. Algebraic multiplicity = Geometric multiplicity = 2. A is not diagonalizable. O A = 2. Algebraic multiplicity = Geometric multiplicity = 2. A = 3. Algebraic multiplicity = Geometric multiplicity = 2. o 1 o o 2 o P: 1 0 2o 20' Fly: 0 2 o o o 1 o o o 1 o o o ENDS WEED