Determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.(a) If A is an m × n matrix, then R(A) and N(AT) are orthogonal subspaces of Rn.(b) The set of all vectors orthogonal to every vector in a subspace S is the orthogonal complement of S.(c) Given an m × n matrix A and a vector b in Rm, the least squares problem is to find x in Rn such that ||Ax = b||2 is minimized.

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