Name: Bryan Murray Account Name: btm6580 Attendance Sheet #: 29

Assignment #: 11 Problem #: 7.2.2

URL: http://acs.tamu.edu/~btm658b/m311p7_2_2.html

a) Calculate the determinant .

b) Does the set {₁ = (2,1,1), ₂ = (1,-2,1), ₃ = (1,-1,1)} form a left-handed or a right-handed basis for R³, or neither.

a) Use cofactor expansion down the first column

= (1)(2) + (-1)(1) + (1)(1)

= (2)(1) + (-1)(2) + (1)(-3)

= 2 + (-2) + (-3)

= 2 – 5

= -3

b) The determinant of matrix formed by these vectors is negative, therefore the vectors form a left-handed coordinated system for R³.