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 kupata determinant ya matrix B, tutatumia njia ya upanuzi wa cofactor. Matrix iliyotolewa ni: B = 1 & 2 & 3 \\ 3 & 2 & 1 \\ 2 & 0 & 2 Step 1: Tumia fomula ya determinant kwa matrix ya 3 × 3. Fomula ya determinant ya matrix a & b & c \\ d & e & f \\ g & h & i ni a(ei - fh) - b(di - fg) + c(dh - eg). Step 2: Badilisha namba kutoka matrix B kwenye fomula. |B| = 1 · 2 & 1 \\ 0 & 2 - 2 · 3 & 1 \\ 2 & 2 + 3 · 3 & 2 \\ 2 & 0 Step 3: Kokotoa determinants za matrix ndogo za 2 × 2. 2 & 1 \\ 0 & 2 = (2 × 2) - (1 × 0) = 4 - 0 = 4 3 & 1 \\ 2 & 2 = (3 × 2) - (1 × 2) = 6 - 2 = 4 3 & 2 \\ 2 & 0 = (3 × 0) - (2 × 2) = 0 - 4 = -4 Step 4: Badilisha matokeo haya kwenye fomula kuu na kurahisisha. |B| = 1 · (4) - 2 · (4) + 3 · (-4) |B| = 4 - 8 - 12 |B| = -4 - 12 |B| = -16 Determinant ya matrix B ni: -16 Tuma swali linalofuata 📸