# 4.10 - MATH1850U/2050U Chapter 4 cont GENERAL VECTOR SPACES...

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MATH1850U/2050U: Chapter 4 cont. .. 1 GENERAL VECTOR SPACES cont. .. Properties of Matrix Transformations (4.10; pg. 263) Recall: Last day, we said that the standard matrix for a transformation can be found using    ) ( | | ) ( | ) ( 2 1 n T T T T e e e . Example: Find the standard matrix for the linear operator 2 2 : R R T that projects a vector onto the x -axis, then contracts that image by a factor of 5. Definition: If we have k n A R R T : and m k B R R T : , we can apply these in succession by finding the composition of T B with T A , denoted by )) ( ( ) )( ( x x w A B A B T T T T to produce a transformation from R n to R m . Example: Say 2 2 1 : R R T is rotation counter-clockwise by 2 / , say 2 2 2 : R R T is projection on the y -axis. Find ) , )( ( 2 1 1 2 x x T T

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MATH1850U/2050U: Chapter 4 cont. .. 2 Example: Example: Find the standard matrix for the linear operator 2 2 : R R T that reflects a vector versus the line
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## This note was uploaded on 10/12/2011 for the course MATH 1020 taught by Professor Paulatu during the Spring '11 term at UOIT.

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4.10 - MATH1850U/2050U Chapter 4 cont GENERAL VECTOR SPACES...

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