Kunze Linear Algebra · Problem 2.6.4

Vector Spaces

Mathematics — Methods · basis-and-coordinates-in-c3

Problem

In C3C^3, let α1=(1,0,−i),α2=(1+i,1−i,1),α3=(i,i,i).\alpha_1 = (1, 0, -i), \quad \alpha_2 = (1+i, 1-i, 1), \quad \alpha_3 = (i, i, i). Prove that these vectors form a basis for C3C^3. What are the coordinates of the vector (a,b,c)(a, b, c) in this basis?

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