Science:Math Exam Resources/Courses/MATH152/April 2011/Question B 04 (a)
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Question B 04 (a) 

Let a=[1,2,1]. Consider the transformation defined by for all x in , where is the crossproduct in . Show that T is a linear transformation. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Recall that a transformation is linear if for some vectors x, y, and constant c. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Following the hint, we seek to show the properties of a linear transformation, For the first property, where we have used that the cross product is distributive over addition. The second property holds by the compatibility of scalar multiplication with the cross product, Therefore we have concluded that T is a linear transformation. 