True or False (justify) a.) If dim(V ) = dim(W), then V and W are isomorphism. b.) There is a linear transformation T : R3 → R2 such that T(1, 0, 3) = (1, 1) and T(−2, 0, −6) = (2, 1). c.) If UT is one-to-one, then T is one-to-one. Must U also be one-to-one?
True or False (justify) a.) If dim(V ) = dim(W), then V and W are isomorphism. b.) There is a linear transformation T : R3 → R2 such that T(1, 0, 3) = (1, 1) and T(−2, 0, −6) = (2, 1). c.) If UT is one-to-one, then T is one-to-one. Must U also be one-to-one?
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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True or False (justify)
a.) If dim(V ) = dim(W), then V and W are isomorphism.
b.) There is a linear transformation T : R3 → R2
such that T(1, 0, 3) = (1, 1) and T(−2, 0, −6) =
(2, 1).
c.) If UT is one-to-one, then T is one-to-one. Must U also be one-to-one?
d.) [T]γβ = [U]γβ implies that T = U.
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