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6. We want T: R² → R³ and S : R³ → R² to be linear transformations defined by matrices A and B so that T(v) = Aʊ and S(u) = Bū. • Create your choice of valid matrices A and B with at least three different non-zero numbers in each matrix. • What is the domain and codomain for SoT? Compute the matrix for this transformation based on your choices for A and B. • Compute S ¤ T(1) where I is either (1,1) or (1,1,1) as appropriate.

6. We want T: R² → R³ and S : R³ → R² to be linear transformations defined by matrices A and B so that T(v) = Aʊ and S(u) = Bū. • Create your choice of valid matrices A and B with at least three different non-zero numbers in each matrix. • What is the domain and codomain for SoT? Compute the matrix for this transformation based on your choices for A and B. • Compute S ¤ T(1) where I is either (1,1) or (1,1,1) as appropriate.

Advanced Engineering Mathematics
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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Linear Alegrba and Differential Equations

6. We want T: R² → R³ and S : R³ → R² to be linear transformations defined by matrices A and B so that T(v) = Aʊ and S(u) = Bū. • Create your choice of valid matrices A and B with at least three different non-zero numbers in each matrix. • What is the domain and codomain for SoT? Compute the matrix for this transformation based on your choices for A and B. • Compute S ¤ T(1) where I is either (1,1) or (1,1,1) as appropriate.
Transcribed Image Text:6. We want T: R² → R³ and S : R³ → R² to be linear transformations defined by matrices A and B so that T(v) = Aʊ and S(u) = Bū. • Create your choice of valid matrices A and B with at least three different non-zero numbers in each matrix. • What is the domain and codomain for SoT? Compute the matrix for this transformation based on your choices for A and B. • Compute S ¤ T(1) where I is either (1,1) or (1,1,1) as appropriate.
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