Let T₁ and T₂ be linear transformations given by 2x1 + x₂ X1 x1 + x₂. 9x1 + 8x2 x1 + x2 Find the matrix A such that the following are true. (a) T₁¹(T₂(x)) = Ax A = 2 1 1 1 x2]. ↓ 1

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 T₁ and T₂ be linear transformations given by
2x1 + x2
T₁([x²]) =
T²([x2₂]) = [₁ [2].
x1 + x2
9x1 + 8x2
x1 + x2
Find the matrix A such that the following are true.
(a)
T₁¹(T₂(x)) = Ax
A =
X
2
1
[x₂
1
1
Transcribed Image Text:Let T₁ and T₂ be linear transformations given by 2x1 + x2 T₁([x²]) = T²([x2₂]) = [₁ [2]. x1 + x2 9x1 + 8x2 x1 + x2 Find the matrix A such that the following are true. (a) T₁¹(T₂(x)) = Ax A = X 2 1 [x₂ 1 1
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