7.2.2

1. Calculate the determinant
2. Does the set {v1=(2,1,1), v2=(1,2,-1), v3=(1,-1,1)} form a left-handed or a right-handed basis for R³, or neither?

Solution:

(a) We start with a formula for the determinant of a 3X3 matrix:

(b) Since the determinant is negative, the set {v1=(2,1,1), v2=(1,2,-1), v3=(1,-1,1)} forms a left-handed basis for R³.

©James Reese [1998]