Question: Let S be the solution set to a consistent system of linear equations Ax = b where b E Rem, A E Mmxn(R), and b

Let S be the solution set to a consistent system of linear equations Ax = b where b E Rem, A E Mmxn(R), and b + 0. Prove or disprove the following statements. (a) For all y, Z ER", if y, Z E S, then y + Z ES. (b) For all y ER", if y E Null(A) and Z E S, then 27 + Z E S. (c) For all y, Z ER", if y, Z E S, then 27 - Z ES

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