Find the eigenvalues and a basis for each eigenspace in C², if A act on C², where A = [a₁ a2], a₁ = (−3, 2), a2 = (−1, −5)Oλ = −4+ i, (1 - i, 2); λ = −4 − i, (1 + i, 2)2-Oλ=4-i, (1 + i, 2) ; λ = 4 + i, (1 − i, 2)-O 2-4 + i, (1 + i, 2); λ = -4 - i, [1 - i, 2)=Oa4-i, (1 - i, 2); λ = 4 + i, [1 + i, 2)Ο=λ = −3+ i, (2 + i, 5); λ = −3 − i, (2 — i, 5)O2 = 3-i, (2 − i, 5); λ = 3 + i, (2 + i, 5)

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C2, if A act on C2, where A = [a1a2], αγ = (-3, 2), a2 = (-1, – 5) = a₂ Ο λ = -4 + i, (1 - i, 2); λ = -4 – i, (1 + i, 2) Ο λ=4-i, (1 + i, 2) ; λ = 4 + i, (1 – i, 2) - Ο λ = -4 + i, (1 + i, 2) ; λ = -4 – i, [1 – i, 2) Ο λ=4-i, (1 – i, 2) ; λ = 4 + i, [1 + i, 2) Ο λ = -3 + i, (2 + i, 5); λ = -3 – i, (2 – i, 5) = - Ο λ = 3 – i, (2 – i, 5) ; λ = 3 + i, (2 + i, 5)

C2, if A act on C2, where A = [a1a2], αγ = (-3, 2), a2 = (-1, – 5) = a₂ Ο λ = -4 + i, (1 - i, 2); λ = -4 – i, (1 + i, 2) Ο λ=4-i, (1 + i, 2) ; λ = 4 + i, (1 – i, 2) - Ο λ = -4 + i, (1 + i, 2) ; λ = -4 – i, [1 – i, 2) Ο λ=4-i, (1 – i, 2) ; λ = 4 + i, [1 + i, 2) Ο λ = -3 + i, (2 + i, 5); λ = -3 – i, (2 – i, 5) = - Ο λ = 3 – i, (2 – i, 5) ; λ = 3 + i, (2 + i, 5)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 44E

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