Introduction

Determinants are most of the time not very useful:

• The system 0.1 x₁ = 0.3, 0.1 x₂ = 0.3, , 0.1 x_n = 0.3 is pefectly well solvable, but |A| will underflow on typical computers for values of n as low as 40.
• Direct evaluation of a determinant of an matrix takes n! multiplications. The big bang was about seconds ago; evaluating a determinant takes 10¹⁰⁰ multiplications. (And allows an interesting possible accumulation of numerical errors.)

Small determinants may be convenient.