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
Huu hapa ni jibu la swali lako la kutumia njia ya matriki: Tunapewa mfumo wa milinganyo: 1) x + y = 5 2) 3x - 2y = 0 Step 1: Andika milinganyo katika mfumo wa matriki AX = B. 1 & 1 \\ 3 & -2 x \\ y = 5 \\ 0 Hapa, A = 1 & 1 \\ 3 & -2 , X = x \\ y , na B = 5 \\ 0 . Step 2: Tafuta kigeuzi (inverse) cha matriki A. Kwanza, tafuta determinant ya A: (A) = (1)(-2) - (1)(3) = -2 - 3 = -5 Kigeuzi cha A ni: A^-1 = (1)/((A)) d & -b \\ -c & a = (1)/(-5) -2 & -1 \\ -3 & 1 A^-1 = (-2)/(-5) & (-1)/(-5) \\ (-3)/(-5) & (1)/(-5) = (2)/(5) & (1)/(5) \\ (3)/(5) & -(1)/(5) Step 3: Tafuta X kwa kutumia X = A^-1B. x \\ y = (2)/(5) & (1)/(5) \\ (3)/(5) & -(1)/(5) 5 \\ 0 Fanya kuzidisha kwa matriki: x = ((2)/(5))(5) + ((1)/(5))(0) = 2 + 0 = 2 y = ((3)/(5))(5) + (-(1)/(5))(0) = 3 + 0 = 3 Hivyo, suluhisho ni: x = 2, y = 3 That's 2 down. 3 left today — send the next one.