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Unformatted text preview: MAS 4105 — Solution to Homework 2 — FALL 2009
Deﬁne T : R2 −→ R2 by T (x, y ) = (y, 2x). We show that T is linear.
Suppose a = (a1 , a2 ) and b = (b1 , b2 ) ∈ R2 and c ∈ R. Then a + b = (a1 + b1 , a2 + b2 )
T (a + b) = (a2 + b2 , 2(a1 + b1 )) = (a2 , 2a1 ) + (b2 , 2b1 ) = T (a) + T (b).
Also ca = (ca1 , ca2 ) and
T (ca) = (ca2 , 2(ca1 ) = c(a2 , 2a1 ) = cT (a).
Hence T is linear. 1 ...
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This note was uploaded on 12/27/2011 for the course MAS 4105 taught by Professor Rudyak during the Spring '09 term at University of Florida.
- Spring '09