Use cofactor expansion to show that the determinant of an n × n matrix

| August 30, 2017

1.Use cofactor expansion to show that the determinant of an n × n matrix is a linear function of its first column. Also show that it is not a linear function of its argument, the matrix itself.

2.Use cofactor expansion to show that the determinant of ann×nmatrix is antisymmetric (meaning it changes by a negative sign) under exchange of its first two columns.

Consider R3 with two orthonormal bases: the canonical basis e = (e1,e2,e3) and the basis f = (f1, f2, f3), where f1 = (1/√3)(1,1,1), f2 = (1/√6)(1,−2,1), f3 = (1/√2)(1,0,−1).
(a) Find the matrix, S, of the change of basis transformation such that [v]f =S[v]e, forallv∈R3, where [v]b denotes the column vector of v with respect to the basis b.

Get a 30 % discount on an order above $ 5
Use the following coupon code:
CHRISTMAS
Order your essay today and save 30% with the discount code: CHRISTMASOrder Now
Positive SSL