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10. Let T: R" → R" be a linear transformation. Prove the following: а. Т(0) 3D 0 b. T(au+ bv) = aT (u) + bT (v) for all u, v e R" and all scalars a and b

10. Let T: R" → R" be a linear transformation. Prove the following: а. Т(0) 3D 0 b. T(au+ bv) = aT (u) + bT (v) for all u, v e R" and all scalars a and b

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 algebra 2.2 Q10

10. Let T: R" → R" be a linear transformation. Prove the following: а. Т(0) — 0 b. T(au + bv) = aT (u) + bT (v) for all u, v e R" and all scalars a and b
Transcribed Image Text:10. Let T: R" → R" be a linear transformation. Prove the following: а. Т(0) — 0 b. T(au + bv) = aT (u) + bT (v) for all u, v e R" and all scalars a and b
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