Use cofactor expansion to show that the determinant

Reference no: EM13873905

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 an n × n matrix 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).
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.

Reference no: EM13873905

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