Let A=(12​−41​) and E be the 2×2 elementary matrix that encodes R1↔R2. (a) Explicitly give det(A). Show your work (witho

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Let A 12 41 And E Be The 2 2 Elementary Matrix That Encodes R1 R2 A Explicitly Give Det A Show Your Work Witho 1 (25.07 KiB) Viewed 51 times

Let A=(12​−41​) and E be the 2×2 elementary matrix that encodes R1↔R2. (a) Explicitly give det(A). Show your work (without uking Matlab/Python, ete.). (b) Explicitly give A−1. Show your work (without using Mutlab/Python, etc.). (c) Explicitly give det (A−3). Show your work (without using Mathab/Python, etc.). Hint: You do not need to compute A−3=(A3)−1=(A−1)3. (d) Explicitly give the characteristic polynomial of A. Show your work. You don't need to solve it. (e) Write down the explicit entries of E. (f) Write down the explicit entries of EA.