All simulators
Solving Ax = b
Two equations as two lines: as the determinant shrinks, the solution becomes fragile and then disappears.
Day 19: Inverses, Determinants & Systems of Equationsx + y = 2.00
x + 1.50·y = 2.50
det A = c − 1
0.500
solution (x, y)
(1.00, 1.00)
condition number
10.4
large = fragile
Each equation is a line; the solution is where they cross. As c → 1 the lines become parallel, det A → 0 and the crossing point races off: a tiny change in b moves the solution a lot. That is ill-conditioning.