Section 5.1:Number 5(c, d, g) only! 5. For each linear operator T on V, find the eigenvalues of T and an orderedbasis for V such that [T] is a diagonal matrix.B(a) VR2 and T(a, b) = (-2a+3b, -10a + 96)(b) VR3 and T(a, b, c) = (7a-4b+ 10c, 4a - 36+ 8c, -2a + b - 2c)(c) VR3 and T(a, b, c) = (-4a+3b-6c, 6a - 76+ 12c, 6a-6b+11c)(d) VP₁(R) and T(ax + b) = (-6a + 2b)x + (-6a + b)(e) VP2(R) and T(f(x)) = xf'(x) + ƒ(2)x + f (3)(f) VP3(R) and T(f(x)) = f(x) + ƒ(2)x(g) VP3(R) and T(f(x)) = xf'(x) + ƒ"(x) − f(2)(h) VM2x2(R) and T(i) VM2x2(R) and TaCbdb=d bC adT (a 2) = (a c)c)b(j) VM2x2(R) and T(A) = A +2 tr(A) 12

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. For each linear operator T on V, find the eigenvalues of T and an ordered basis ẞ for V such that [T] is a diagonal matrix. - 3b+8c,-2a+b2c) (a) VR2 and T(a, b) = (-2a + 3b, -10a + 9b) (b) VR3 and T(a, b, c) = (7a-4b+ 10c, 4a (c) VR3 and T(a, b, c) = (-4a+3b-6c, 6a- 76+12c, 6a-6b+11c) (d) V P₁(R) and T(ax + b) = (-6a+ 2b)x + (-6a+b) = == (e) VP2(R) and T(f(x)) = xf'(x) + f(2)x+ƒ(3) (f) VP3(R) and T(f(x)) = f(x) + f(2)x (g) VP3(R) and T(f(x)) = xf'(x) + f"(x) − f(2) (h) VM2x2(R) and T (i) VM2x2(R) and T ( a )) = ( c b) ( a c ) = ( å i ) . b (j) VM2x2(R) and T(A) = A +2 tr(A) 12

. For each linear operator T on V, find the eigenvalues of T and an ordered basis ẞ for V such that [T] is a diagonal matrix. - 3b+8c,-2a+b2c) (a) VR2 and T(a, b) = (-2a + 3b, -10a + 9b) (b) VR3 and T(a, b, c) = (7a-4b+ 10c, 4a (c) VR3 and T(a, b, c) = (-4a+3b-6c, 6a- 76+12c, 6a-6b+11c) (d) V P₁(R) and T(ax + b) = (-6a+ 2b)x + (-6a+b) = == (e) VP2(R) and T(f(x)) = xf'(x) + f(2)x+ƒ(3) (f) VP3(R) and T(f(x)) = f(x) + f(2)x (g) VP3(R) and T(f(x)) = xf'(x) + f"(x) − f(2) (h) VM2x2(R) and T (i) VM2x2(R) and T ( a )) = ( c b) ( a c ) = ( å i ) . b (j) VM2x2(R) and T(A) = A +2 tr(A) 12

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.6: The Algebra Of Matrices

Problem 13E

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