Kunze Linear Algebra · Problem 3.1.5

Linear Transformations

Mathematics — Methods · existence-linear-transformation-consistency

Problem

If α1=(1,−1),β1=(1,0)\alpha_1 = (1, -1), \quad \beta_1 = (1, 0) α2=(2,−1),β2=(0,1)\alpha_2 = (2, -1), \quad \beta_2 = (0, 1) α3=(−3,2),β3=(1,1)\alpha_3 = (-3, 2), \quad \beta_3 = (1, 1) is there a linear transformation TT from R2R^2 into R2R^2 such that Tαi=βiT\alpha_i = \beta_i for i=1,2i = 1, 2 and 33?

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