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Suppose that T: R³ → R³ is a linear transformation. Use properties of vector arithmetic and the VER³ using only T(e), 7(e₂), linearity of T' to explain why we can compute T (v) for any →>>> T (e) where ei is a standard basis vector (all entries are zeros except for a 1 in the i-th position).

Suppose that T: R³ → R³ is a linear transformation. Use properties of vector arithmetic and the VER³ using only T(e), 7(e₂), linearity of T' to explain why we can compute T (v) for any →>>> T (e) where ei is a standard basis vector (all entries are zeros except for a 1 in the i-th position).

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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→>> Suppose that T: R³ → R³ is a linear transformation. Use properties of vector arithmetic and the linearity of T' to explain why we can compute T (v) for any v ER³ using only 7 (₁), T (₂), T (e) where e; is a standard basis vector (all entries are zeros except for a 1 in the i-th position).
Transcribed Image Text:→>> Suppose that T: R³ → R³ is a linear transformation. Use properties of vector arithmetic and the linearity of T' to explain why we can compute T (v) for any v ER³ using only 7 (₁), T (₂), T (e) where e; is a standard basis vector (all entries are zeros except for a 1 in the i-th position).
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