Let S: R²- → R² and T: R² → R² be linear transformations such that 4 As = [2²] and AS-T = [3/2 3/2] where S T is the composition of S and T. Then T is the function whose matrix AT is given by [2√3/2 3/2 1 ° [3³/2 J 3 3/2 3 3/2 " 4 [123] ° [21][3/2 3/2] There are infinitely many possible functions T.
Let S: R²- → R² and T: R² → R² be linear transformations such that 4 As = [2²] and AS-T = [3/2 3/2] where S T is the composition of S and T. Then T is the function whose matrix AT is given by [2√3/2 3/2 1 ° [3³/2 J 3 3/2 3 3/2 " 4 [123] ° [21][3/2 3/2] There are infinitely many possible functions T.
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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Let S:R2→R2 and T:R2→R2 be linear transformations such that
Transcribed Image Text:Let S: R?
→ R? and T: R² → R? be linear transformations such that
4
2
and As-T
1
3
3
As
3/2
3/2
where S • T is the composition of S and T . Then T is the function whose
matrix AT is given by
3
3/2
3/2
3
-1
4
3
2
3/2
3/2
2
2
3
3
3/2
3/2
O There are infinitely many possible functions T .
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