6. Let A = point) 7. If A = -3 20 3 1 0 52 a)...

 

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6. Let A = point) 7. If A = -3 20 3 1 0 52 a) A = 131 -3] L 12 and B 4 2 1 132 and AB = a 8. Let u = --[1] -3 9. Determine which matrix is invertible. (1 point): 2 and v= b 2 02 a) 3 -1 0 ; b) 4 02 10. Find A-¹ if (1 point): -3 ·[ . Find B (1 point). 17 Compute uv, vu, uv", and vu". 1 1 1 2 3 1 121 ; c) Find A+ B, A- B, AB and BA (1 [ 1 0 1 1 1 0; d) 01 1 0 1 2 1 1 0; b) A = 2 0 1 ; c) A = 0 1 1 102 Extra credits. El Prove that if A, B, and C are matrices then: (2 3 4 -1 0 1-2 2 0 -1 0 1 0 0008 0 1 a 0 01 a 0 001 a 0001 points) a) (AT)-¹ = (A-¹); b) (A-¹)-¹ = A; c) (kA)-¹ = A-¹, k0; d) (ABC)-¹ = C-¹B-¹A-¹. 6. Let A = point) 7. If A = -3 20 3 1 0 52 a) A = 131 -3] L 12 and B 4 2 1 132 and AB = a 8. Let u = --[1] -3 9. Determine which matrix is invertible. (1 point): 2 and v= b 2 02 a) 3 -1 0 ; b) 4 02 10. Find A-¹ if (1 point): -3 ·[ . Find B (1 point). 17 Compute uv, vu, uv", and vu". 1 1 1 2 3 1 121 ; c) Find A+ B, A- B, AB and BA (1 [ 1 0 1 1 1 0; d) 01 1 0 1 2 1 1 0; b) A = 2 0 1 ; c) A = 0 1 1 102 Extra credits. El Prove that if A, B, and C are matrices then: (2 3 4 -1 0 1-2 2 0 -1 0 1 0 0008 0 1 a 0 01 a 0 001 a 0001 points) a) (AT)-¹ = (A-¹); b) (A-¹)-¹ = A; c) (kA)-¹ = A-¹, k0; d) (ABC)-¹ = C-¹B-¹A-¹.