선형대수학 (1) - 1차 연립방정식과 가우스소거법

Linearity : f(x), operation

1. Superposition : f(x1+x2) = f(x1) + f(x2)
2. Homogeniety : f(ax) = a f(x)

→  f(a1xa + a2x2) =a1f(xa) +a2f(x2)

→  f(k=1nakxk) = k=1nak f(xk)

Vector(Column Vector)

Singular Case

• No solution
• Infinite solutions

1. row form(직선, 평면으로)

→ parallel (no solution)

→ overlap (infinite solutions)

2. column form(column vector 형태)

Gauss Elimination(가우스 소거법, GE)

all pivots are non-zero → a unique solution

Breakdown

• when a zero appears in a pivot position
• GE has to stop
• the order of equations has to be changed