Let T: R² R² be defined by T [T] Let B: 5 = {¹₁ = [ 3 ], ¹₂ = [ º ], } and C = {v₁ = [1] ₁ V₂ = []} {u V2 -H]} 3 = ([22]) = [. X2 Find [T], the matrix representation of T with respect to the bases B and C. x1 x1 X2 Ex: 5

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let T: R²
R² be defined by T
[T]
Let B:
5 = {¹₁ = [ 3 ], ¹₂ = [ º ], } and C = {v₁ = [1] ₁ V₂ = []}
{u
V2
-H]}
3
=
([22]) = [.
X2
Find [T], the matrix representation of T with respect to the bases B and C.
x1
x1 X2
Ex: 5
Transcribed Image Text:Let T: R² R² be defined by T [T] Let B: 5 = {¹₁ = [ 3 ], ¹₂ = [ º ], } and C = {v₁ = [1] ₁ V₂ = []} {u V2 -H]} 3 = ([22]) = [. X2 Find [T], the matrix representation of T with respect to the bases B and C. x1 x1 X2 Ex: 5
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Let T: P₂ → P₁ be defined by T(p(x)) = p'(x).
Let B = { 1 + x + x², 1 + x, 1} and C = {1 − 3x, 1 – 2x}.
Find [7], the matrix representation of Twith respect to the bases B and C.
[T]
=
Ex: 5
Transcribed Image Text:Let T: P₂ → P₁ be defined by T(p(x)) = p'(x). Let B = { 1 + x + x², 1 + x, 1} and C = {1 − 3x, 1 – 2x}. Find [7], the matrix representation of Twith respect to the bases B and C. [T] = Ex: 5
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