Linear algebra essentials
Đã giới thiệu| English | Ý nghĩa |
|---|---|
| determinant/dɪˈtɜːmɪnənt/ | determinant |
| linear system/ˈlɪnɪə ˈsɪstəm/ | linear system |
| singular/ˈsɪŋɡjʊlə/ | singular |
Elimination and the determinant
- A linear system 线性方程组 solves by elimination; the inverse route verifies it. $det = 0$ means singular 奇异 — no unique solution, a floating node in circuit terms.
- Nodal analysis IS
Ax = b: the determinant is a circuit-debugging tool.
{exercise:uni-ee2x-linear}

A 2×2 system's coefficient determinant is zero. In circuit terms this most likely means —
Độ khó 1/5 · 100 xu + phần thưởng nhỏ khi hoàn thành lần đầu tiên hôm nay
det = 0 means the equations are dependent — the model double-counts one constraint (or misses a ground); the physics needs re-modelling, not just re-solving.
The system x+2y=8, 2x+4y=16 has —
Độ khó 1/5 · 100 xu + phần thưởng nhỏ khi hoàn thành lần đầu tiên hôm nay
det = 1x4 - 2x2 = 0 and the equations are consistent (the second is twice the first), so a whole line of solutions - the determinant cannot tell no-solution from infinite; consistency does.
The mesh system [[6,-4],[-4,10]] i = [12,-3] solves to —
Độ khó 1/5 · 100 xu + phần thưởng nhỏ khi hoàn thành lần đầu tiên hôm nay
det = 6x10 - 16 = 44, so unique; elimination (or the inverse) gives 2.455 and 0.682, verified by substitution to machine precision. The -4 off-diagonals are the shared resistor: coupling lives off the diagonal.