MATH221 April 2010
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Question 01 (d)
Then the matrix U is an echelon form for A (you may assume this, you don't have to do the row reduction again.)
Solve the equation
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Find the reduced echelon form, that is, use row operations to set the entries above the pivot elements to zero.
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In order to solve we need to find the reduced echelon form. Starting with the echelon form , we first subtract the second row from the first row twice, , to obtain
Now we add the third row eight times to the first row, and subtract the third row three times from the second row, , , to obtain
In plain notation this means that
Fixing the pivot variables and solving the above for the remaining two variables we find that the solution to has the form
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