Engineering Calculus Notes 432

# Engineering Calculus Notes 432 - 420 CHAPTER 4. MAPPINGS...

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Unformatted text preview: 420 CHAPTER 4. MAPPINGS AND TRANSFORMATIONS Remark 4.1.3. The composition of linear maps is linear, and the matrix representative of the composition is the product of their matrix representatives. For example, suppose L′: R3 → R2 is deﬁned by x L′ y = z x+y y+z and L: R2 → R3 is deﬁned by L x y x−y = x+ y ; 2x − y then L ◦ L′: R3 → R3 is deﬁned by x (L ◦ L′ ) y = L z x+y y+z (x + y ) − (y + z ) = (x + y ) + (y + z ) 2(x + y ) − (y + z ) x−z = x + 2y + z 2x + y − z and the composition in the other order, L′ ◦ L: R2 → R2 is deﬁned by (L′ ◦ L) x y x−y = L′ x + y 2x − y = = (x − y ) + (x + y ) (x + y ) + (2x − y ) 2x 3x + 2y . ...
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## This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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