Don\'t look at these until you\'ve given the whole practice exam your best attem

Question

Don't look at these until you've given the whole practice exam your best attempt! (1) (60 points) Consider the system of linear equations (a) (14) WTILe l his system in trial rix forrn as an equil.lon Ax-b. Where A is a lnatrix ud ¢ and b are vectors. Then write the system as an augnented matrix 3 12 3 The ('Tresponding a.l lginerted matrix is 1 -3 4 4 1 41 0 3 12 3 1 (b) (14) What is the first st you would take in order to perfortio on this system in the second ngnation? Perf rm this step assuming your first goal is to eliminate the showing all work. The fust eliuination ste is to subtract -1 ti to row 2). his yield:s row 1 fro row 2 (in other words, add rw 1 1 3 4 4 11011015 -3 12 3 1 3 12 3 1 (c) Write your elimination step from (b) as a matrix E. Once you perform the elimination step on the matrix A, is the resulting matrix equal to EA, AE, both, or neither? Explain. (i) The elimination matrix in this case is the result of performing the operation "subtract -1 times row 1 from row 2" (aka·add row 1 to row 2") on the 3 x 3 identity matrix. In other words E=11 10 (ii) The mat rix resulting after performing this tirst elimination step is EA, because elimination matrices act on the left (when we want to perform row operations). It's not AE because 1 -2 1

Explanation / Answer

Actually AE gives different result than EA and the answer you see in C(2) is multiplying transpose of E on the right side of A...

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