5. Let S : R³ R2 and T: R² ->> X1 2 X1 $8-0-0-- .T = X2X3 S x2 R2 be defined by X3 X1 X2 = x1 + 3x₂ - X1 2x2 Verify whether each of the composition SoT and To S exists, and find an image of either of them if they exist.
5. Let S : R³ R2 and T: R² ->> X1 2 X1 $8-0-0-- .T = X2X3 S x2 R2 be defined by X3 X1 X2 = x1 + 3x₂ - X1 2x2 Verify whether each of the composition SoT and To S exists, and find an image of either of them if they exist.
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:5. Let S : R³ →→→→ R² and T : R² -
X1
2
X1
X1
•B¬M«N-R*
T
X2X3
X2
S x2
R2 be defined by
X3
=
x₁ + 3x₂
2x2 X1
Verify whether each of the composition SoT and To S exists, and find an image of
either of them if they exist.
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