MATH221 April 2010
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Question 01 (f)
Then the matrix U is an echelon form for A (you may assume this, you don't have to do the row reduction again.)
Let be the columns of A. Express as a linear combination of the columns of
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1.) To express as a linear combination of and , we take n multiples of each vector that will add up to .
2.) One way to do this is by putting the vectors in a system of equations and then putting this system of equations into an augmented matrix:
+ 2 - 2 = 4 0+ + 3 = -2 0 + 0 + = 2
3.) Reduce to row echelon form through these steps: 1.) = -3 2.) = + 2 3.) = - 2
and you will get:
4.) This shows the linear combination:
= 24 = -8 = 2
= 24 - 8 + 2
PROOF: = 24 - 8+ 2
= - +