A basis v1,...,vn of Rn is called right handed if the n n matrix A =

A basis v1,...,vn of Rn is called right handed if the n × n matrix A = (vi €¢€¢€¢ vn) whose columns are the basis vectors has positive determinant: det A > 0. If det A (a) Which of the following form right handed bases of R3?
(i)

(ii)

(iii)

(iv)

(b) Show that if v1, v2, v3 is a left handed basis of R3, then v2, v1, v3 and - v1, v2, v3 are both right handed bases.
(c) What sort of basis has det A = 0?

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