3. [8 marks] (a) Consider the following two 2 × 2 matrices: 12 (23) and B = A = (23) -2 -5 Find by hand A-¹BT +2I and (2

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3 8 Marks A Consider The Following Two 2 2 Matrices 12 23 And B A 23 2 5 Find By Hand A Bt 2i And 2 1 (91.39 KiB) Viewed 61 times

3. [8 marks] (a) Consider the following two 2 × 2 matrices: 12 (23) and B = A = (23) -2 -5 Find by hand A-¹BT +2I and (2A + BT)−¹, and verify that (A¯¹B¹ +21)−¹ (2A+BT)-¹A = by evaluating both sides of the equation. (b) Now suppose that A and B are arbitrary n×n matrices such that A and 2A+BT are invertible. Using general properties of matrix operations (Tables 5.1-5.4 in the Unit Notes), show that (A-¹BT +21)−¹ (2A + BT)-¹A. Show all the steps. =