Determinants and Numerical Approximations to Zero

Start by building a routine to make vectors containing six random numbers on the interval {-1,1}:

Now use rv to make a 6 x 6 matrix, then find its determinant:

Switching two rows changes the sign but not the magnitude of the determinant:

Multiply one row by a constant and calculate determinant:

Multiply two rows by a constant and calculate determinant:

Multiply all rows by a constant and calculate determinant:

Example of numerical precision: if one row of a 6 x 6 matrix is a linear combination of the other five rows, its determinant should evaluate to zero…

However, numerical precision does

Created by Wolfram Mathematica 6.0  (06 September 2007)