Science:Math Exam Resources/Courses/MATH307/December 2006/Question 02 (a)
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Question 02 (a)
Consider the matrix
(a) Find a basis for the nullspace of A.
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Science:Math Exam Resources/Courses/MATH307/December 2006/Question 02 (a)/Hint 1
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To find the basis of null space of A, we solve
This can be done by finding the reduced row echelon form of A as follows:
First, subtract the first row twice from the second row and once from the first row.
Then, divide the second row by 3 and add it to the third row
From this we can see that column 1 and column 3 are the only pivot columns and so the free variables are x2, x4 and x5, while the basic variables are x1 and x3
Solving this r.r.e.f of A for homogeneous solution gives us
Note: we can use matlab command null (rref(A), ’r’) to directly calculate the basis of null space for this matrix A