MATH307 December 2006
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Question 02 (c)
Consider the matrix
(c) Find a basis for the left nullspace of A.
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To find the basis of left nullspace, , we solve for
This can be done by finding the row echelon form of
Perform the following row operations:
- row 2 = row 2 - row 1
- row 4 = row 4 row 1
- row 5 = row 5 row 1
and we get the matrix :
Further row operations,
- row 4 = row 4 row3
- row 5 = row 5 row 3
and interchanging row 2 and 3 gives us the row echelon form of the matrix as:
From this we can see that only is a free variable.
Solving this row echelon for homogeneous solution gives us :
Thus a basis of is given by