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ECE 280: Electrical Engineering Analysis Homework Set #2; Points Possible: 100 Due: 6PM, Friday, January 31, 2020 For each of the following problems, do your work by hand unless specifically told to use Matlab. Be sure to show all your work! 1. (25 pt) Let 𝐴𝐴 = 1 3 4 0 2 7 1 5 3 (a) Compute the adjugate matrix 𝐶𝐶 (b) Compute �𝐴𝐴 by expanding in minors using the second row. (c) Compute �𝐴𝐴 by expanding in minors using the second column. (d) Computer 𝐴𝐴 −1 (the inverse of 𝐴𝐴 (e) Computer 𝐴𝐴 −1 using Matlab (f) Verify that the second row of 𝐵𝐵 = 𝐴𝐴 𝐴𝐴 −1 is the second row of 𝐼𝐼 2. (20 pts) Consider the system of equations 𝑥𝑥 1 + 3 𝑥𝑥 2 4 𝑥𝑥 3 = 0 2 𝑥𝑥 2 + 7 𝑥𝑥 3 = 1 𝑥𝑥 1 + 5 𝑥𝑥 2 3 𝑥𝑥 3 = 2 Note: the coefficient matrix is the same as 𝐴𝐴 in Problem 1. (a) Solve for 𝑥𝑥 1 , 𝑥𝑥 2 , 𝑥𝑥 3 using Cramer’s rule. (b) Solve for 𝑥𝑥 1 , 𝑥𝑥 2 , 𝑥𝑥 3 using 𝑋𝑋 = 𝐴𝐴 −1 𝐵𝐵 (c) In Matlab , solve for 𝑥𝑥 1 , 𝑥𝑥 2 , 𝑥𝑥 3 using Gaussian elimination. (d) In Matlab , solve for 𝑥𝑥 1 , 𝑥𝑥 2 , 𝑥𝑥 3 using 𝑋𝑋 = 𝐴𝐴 −1 3. (20 pts) Let 𝐴𝐴 = 1 2 0 𝑔𝑔 4 0 1 0 2 (a) Find 𝑔𝑔 so that matrix equation 𝐴𝐴 𝑋𝑋 = 0 has non-trivial solutions. (Hint: if 𝐴𝐴 𝑋𝑋 = 0 has non-trivial solutions, . ). . . . 𝐵𝐵 .

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