Mathegoras

Vectors and matrices › Rank, eigenvalues and linear maps › Coordinates in a basis

Coordinates of a vector in R^4

University · ●○○○○ 10 pts

Let a1=[1,1,0,0]a_1 = [1, 1, 0, 0], a2=[0,1,1,0]a_2 = [0, 1, 1, 0] and a3=[0,0,1,1]a_3 = [0, 0, 1, 1]. Find the coefficients α1,α2,α3\alpha_1, \alpha_2, \alpha_3 such that v=[1,3,5,3]=α1a1+α2a2+α3a3v = [1, 3, 5, 3] = \alpha_1 a_1 + \alpha_2 a_2 + \alpha_3 a_3, that is, find the coordinate representation [α1,α2,α3][\alpha_1, \alpha_2, \alpha_3] of vv.

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linear combinationssystems of linear equations