4 [5], 9 (a) Write b as a linear combination of a₁ and a2. Let al b a2 = -8 7 and T(a₂) and b = 2 [3] a2. (b) If T: R² → R² is a linear combination such that 9 T(a₁) = [1] 9 52 - 84 a₁ + find T(b).

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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Question
22
8
[]
[7³]
(a) Write b as a linear combination of a₁ and a2.
Let ai
b
=
=
T(b)
=
a2 =
and T(a₂)
Check Answer
and b
2
(b) lf T: R² → R² is a linear combination such that
T(2₁) = [1]
find T(b).
=
a2.
=
52
[-534]
84
a₁ +
Transcribed Image Text:8 [] [7³] (a) Write b as a linear combination of a₁ and a2. Let ai b = = T(b) = a2 = and T(a₂) Check Answer and b 2 (b) lf T: R² → R² is a linear combination such that T(2₁) = [1] find T(b). = a2. = 52 [-534] 84 a₁ +
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