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Let S = {v1, v2, v3, v4} be a given basis of R ^4 . Suppose...

Let S = {v1, v2, v3, v4} be a given basis of R ^4 . Suppose that A is a (3 × 4) matrix with the following properties: Av1 = 0, A(v1 + 2v4) = 0, Av2 =[ 1 1 1 ] T , Av3 = [ 0 −1 −4 ]T . Find a basis for N (A), and a basis for R(A). Fully justify your answer.

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