Give the elementary matrix that converts [-2,-2,-1,-3,-1,-3,1,-4,-3] to [-6,-2,-1,-5,-1,-3,-7,-4,-3]

Question
Matrix transformations
asked 2021-03-07
Give the elementary matrix that converts
[-2,-2,-1,-3,-1,-3,1,-4,-3] to [-6,-2,-1,-5,-1,-3,-7,-4,-3]

Answers (1)

2021-03-08
Notice that the difference between the two matrices is that the latter's first row is
(−2,−3,1)+2(−2,−1,−4)=(−6,−5,−7)
Looking over your elementary matrix types, we see that the one that adds 2 times the second row to the first looks something like this.
[1,0,0,2,1,0,0,0,1]
That is, to add row k times row ii to row j, you take the identity matrix and add a k to column ii and row j.
We can multiply it out to confirm
[-6,-2,-1,-5,-1,-3,-7,-4,-3]
0

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