Question:

Question 7 (8 points) [1 c 0] For which conditions of a, b, and c the matrix A = 2 -1 6 is 5 a 3 invertible. A/Problem 7 For which conditions of a, b and c the matrix A = 5 3 is invertible. Solution b -6 3 -3 6 a -R1+R2 -> R2 3R1+R3 -> R3 6 1 b -6 0 c-b 9 0 6+3b a-18 R2/(c-b) -> R2 1 b -6 0 1 9/(c-b) 0 6+3b a-18 (6+3b) R2+R3->R3 b -6 0 1 9/(c-b) 0 0 a-18+(-9)/(c-b)*(6+b) Conditions: a-18+(-9)/(c-b)*(6+b) # 0 c # b