Question: Prove: If A is an m n matrix and x Rn, then either Ax = 0 or there exists y R(AT) such

Prove: If A is an m × n matrix and x ∈ Rn, then either Ax = 0 or there exists y ∈ R(AT) such that xTy ≠ 0. Draw a picture similar to Figure 5.2.2 to illustrate this result geometrically for the case where N(A) is a two-dimensional subspace of R3.

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