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THEOREM 5.2 Suppose TV → W is a linear transformation. at nie "I of SW 2101 1. T(0) = 0. 2. T(-u) = -T(v) for any u in V. 3. T(u-v) = T(u) - T(v) for any u and u in V. 4. T(C₁v₁ + C₂02 + ... + Ck Uk) = C₁T (v₁) + C₂T (v₂) + + CKT (Uk) for any scalars C₁, C2, ..., ck and any vectors V₁, V2, ..., Uk in V.

THEOREM 5.2 Suppose TV → W is a linear transformation. at nie "I of SW 2101 1. T(0) = 0. 2. T(-u) = -T(v) for any u in V. 3. T(u-v) = T(u) - T(v) for any u and u in V. 4. T(C₁v₁ + C₂02 + ... + Ck Uk) = C₁T (v₁) + C₂T (v₂) + + CKT (Uk) for any scalars C₁, C2, ..., ck and any vectors V₁, V2, ..., Uk in V.

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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14. Prove the following parts of Theorem 5.2. 0 a) Part (3) b) Part (4)
Transcribed Image Text:14. Prove the following parts of Theorem 5.2. 0 a) Part (3) b) Part (4)
THEOREM 5.2 Suppose T V W is a linear transformation. 1. T(0) = 0. 2. T(-v) = -T(v) for any v in V. 3. T(uv) = T(u) - T(v) for any u and u in V. 4. ... · T(C₁v₁ + C₂0₂ + + Ck Uk) = C₁T (v₁) + C₂T (v₂)+...+ CKT (Uk) for any scalars C₁, C2, ..., Ck and any vectors V₁, V2, ..., Uk in V. a fost ni ai " of "St oko
Transcribed Image Text:THEOREM 5.2 Suppose T V W is a linear transformation. 1. T(0) = 0. 2. T(-v) = -T(v) for any v in V. 3. T(uv) = T(u) - T(v) for any u and u in V. 4. ... · T(C₁v₁ + C₂0₂ + + Ck Uk) = C₁T (v₁) + C₂T (v₂)+...+ CKT (Uk) for any scalars C₁, C2, ..., Ck and any vectors V₁, V2, ..., Uk in V. a fost ni ai " of "St oko
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