Science:Math Exam Resources/Courses/MATH221/April 2009/Question 05
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Question 05 

Let
Find a basis for and a basis for the orthogonal complement 
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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 

Science:Math Exam Resources/Courses/MATH221/April 2009/Question 05/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. To find a basis for W, we take these 4 vectors and form a matrix A: A = and take rref(A) to get the reduced row echelon form of A: rref(A) = Since only the first 2 columns are pivot, a basis for W is: To find a basis for the orthogonal complement of W, we need find the null space of the matrix B: B = rref(B) = Therefore, a basis for the orthogonal complement of W is: 