![a) Find the inverse of the matrix [5 -3; -3 4]. b) Hence solve the simultaneous equation using the matrix method. 8x+6y=12, 6x+10y=10](/_next/image?url=https%3A%2F%2Fohijasnjvprzodcmxltt.supabase.co%2Fstorage%2Fv1%2Fobject%2Fpublic%2Fwhatsapp-images%2F1786994666016-e3ac1176ddbe408f.png&w=3840&q=75)
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Ili kutatua milinganyo shirikishi kwa kutumia njia ya matriki, tunafuata hatua hizi: Step 1: Andika milinganyo katika mfumo wa matriki. Milinganyo ni: 8x+6y=12 6x+10y=10 Hii inaweza kuandikwa kama AX=B: 8 & 6 \\ 6 & 10 x \\ y = 12 \\ 10 Hapa, A = 8 & 6 \\ 6 & 10 , X = x \\ y , na B = 12 \\ 10 . Step 2: Tafuta kinyume cha matriki A (A^-1). Kwa matriki A = a & b \\ c & d , kinyume chake ni A^-1 = (1)/((A)) d & -b \\ -c & a . Kwanza, tafuta determinant ya A: (A) = (8)(10) - (6)(6) = 80 - 36 = 44 Sasa, tafuta kinyume cha A: A^-1 = (1)/(44) 10 & -6 \\ -6 & 8 Step 3: Tatua kwa X kwa kutumia X = A^-1B. x \\ y = (1)/(44) 10 & -6 \\ -6 & 8 12 \\ 10 Fanya kuzidisha kwa matriki: x \\ y = (1)/(44) (10)(12) + (-6)(10) \\ (-6)(12) + (8)(10) x \\ y = (1)/(44) 120 - 60 \\ -72 + 80 x \\ y = (1)/(44) 60 \\ 8 Zidisha kwa (1)/(44): x \\ y = (60)/(44) \\ (8)/(44) Step 4: Rahisisha majibu. x = (60)/(44) = (15)/(11) y = (8)/(44) = (2)/(11) Kwa hiyo, majibu ni: x = (15)/(11), y = (2)/(11) Tuma swali linalofuata 📸