Find formula for a linear transformation and find bases for kernel and range of the transformation

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Question: Suppose T: R² → R² is a linear operator with T ([1,2]) = [1, 1] and T ([2,0]) = [2, −4].
Give a formula T([x, y]) for any[x, y] ∈ R² . Also find a basis for ker(T), a basis for range(T) and verify the dimension theorem

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Answered By:

Andrew D.
Bachelor's degree in mathematics with tutoring experience

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