1. Recall that an elementary matrix E is any matrix obtained by performing an elementary row operation on the identity m
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1. Recall that an elementary matrix E is any matrix obtained by performing an elementary row operation on the identity matrix. (a) What are the three types of elementary row operations? (b) Note that 1 -2 0 1 0 0 Ei = 0 1 0 E2 = 0 0 1 0 0 1 0 1 0 7 are elementary matrices. Which elementary (row) operation does El correspond to? Which elementary (row) operation does E2 correspond to? (c) Let A= 021 031 011 a12 a13 022 023 032 033 Compute AE, and AE2, where E1, E2 are as in part (b). (d) One can define an elementary column operation to be just like an elementary row operation, but instead of working with rows, we now work with columns. What elementary column operation can be applied to 13 in order to obtain the matrix Ej? What elementary column operations can be applied to 13 in order to obtain the matrix E2? How do these compare with the answers in part (c)?