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# For the A matrix below, find an elementary matrix that will do one step of row reduction to get a zero in the A21 position by using row 1 and row 2....

4. For the A matrix below, find an elementary matrix that will do one step of row reduction to get a zero in the A21 position by using row 1 and row 2. Multiply this by A and call the new matrix B. Now find the elementary matrix that will put a zeros in the B31 position. Multiply it by B and call the new matrix C. Finally, find the elementary matrix that will put a zeros in the C32 position. Your matrix should now be upper triangular. Call it U.

(ii) Now that you have found the elementary matrices, find their inverses (remember you can just change the sign of the off-diagonal element, but check this).

(iii) Multiply the inverses of the elementary matrices in reverse order to find an lower triangular matrix, L. Verify that L*U = A.