Show that the following set of matrices is closed under affine combina- tions. -{(8₂2): ADER} a, b b 0 a S₂ = i.e. Show that c₁ M₁+C₂M₂ E S₂ for all choices M₁, M₂ € S₂ and C₁, C2 ER satisfying C₁+C₂ = 1.
Show that the following set of matrices is closed under affine combina- tions. -{(8₂2): ADER} a, b b 0 a S₂ = i.e. Show that c₁ M₁+C₂M₂ E S₂ for all choices M₁, M₂ € S₂ and C₁, C2 ER satisfying C₁+C₂ = 1.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Show that the following set of matrices is closed under affine combina-
tions.
a 2
-{(33) : abER}.
a,
b
S₂ =
i.e. Show that c₁ M₁+₂ M₂ € S₂ for all choices M₁, M₂ € S₂ and C₁, C2 ER
satisfying C₁+C₂ = 1.
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