Science:Math Exam Resources/Courses/MATH307/December 2012/Question 03 (c)
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Question 03 (c) 

Let be the subspace of vectors in whose components sum to zero. (c) Find a matrix B so that R(B) = S. 
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 

The range of a matrix B is the set of all possible linear combinations of its column vectors. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Since S is the set of all possible linear combinations of its basis vectors, and R(B) is the set of all possible linear combinations of its columns, we can simply populate the columns of B with (nontrivial linear combinations of) the basis vectors of S. For example or 