Question

Question 16 O pts 9x – 2y = 4 Solve the system using inverse of the coefficient matrix. 2x + 4y = 7 9 -2 Where A and B (Hint: find x. x = A-1B). 2 4 7 09

Answer 1

The given system m of equation 9x - 2y = 4 - 2x + 4y =7 can be written This system of equation 2 9 2 4 JE] - [*] 7 AX=B wherle, A- [?]..[] Now, AX=B => AAX = AB X = AB [A A = I ie, we have, 2 4 У adj (A) Now, A-1 = det (A) 9 -2 det (A) = 2 4 (9x4) - 26-2) 36+4 40

det (A) = 40 2 1 - 2 now, ada (A) = [- Ato [5] -4x40 An 2x70 gx to [2x 40 120 A) [-vie Vio - 1/20 9/40 120 so, from (in) we get, -710 -1/20 9190 (110 X 4) + (720 *7) [ (-1/20 x 4) + (740x7) 9/10 + 720 21 -4/20+ 63/40 15/20 55/40 [] [%] 3/4 11/8

Hence, of matrices we get, the equality by the x= 314, y=11/8 so, the required solution is y = 1 11 3 4 x=