Science:Math Exam Resources/Courses/MATH221/April 2009/Question 05
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Find a basis for and a basis for the orthogonal complement
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Science:Math Exam Resources/Courses/MATH221/April 2009/Question 05/Hint 1
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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 =
Therefore, a basis for the orthogonal complement of W is: