c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This] A a 5x5 real matrix & v₁,..., v, linearly independent real vectors in 5 dimensional space: Av₁ = 4v₁ Av₂ = 4v₂ Av3 = -13v3 A(v₁ +vi)=(5-7i) (v₁ +vi)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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find the stretch and if it rotates 0 or 180 degrees for these specific spans! It can be complex!

c)
[For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This]
A a 5x5 real matrix & v₁,..., v5 linearly independent real vectors in 5 dimensional space:
Av₁ = 4v₁
Av₂
Av3 = -13v3
A(v₁ +vši)=(5−7i)(v₁ +vši)
= 4v₂
Transcribed Image Text:c) [For Susan Foreman of 76 Totter's Lane, Coal Hill School, 1963, WHO Could See This] A a 5x5 real matrix & v₁,..., v5 linearly independent real vectors in 5 dimensional space: Av₁ = 4v₁ Av₂ Av3 = -13v3 A(v₁ +vši)=(5−7i)(v₁ +vši) = 4v₂
Al span {V₁, V₂} = Stretch:
Rotationi
A/span {V₁₁ V4} = Stretch:
rotation:
A / Span {√₁}=
5
stretch:
Rotation:
Transcribed Image Text:Al span {V₁, V₂} = Stretch: Rotationi A/span {V₁₁ V4} = Stretch: rotation: A / Span {√₁}= 5 stretch: Rotation:
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