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Let A be a given (3 × 3) matrix, and consider the equation Ax = c,...

Let A be a given (3 × 3) matrix, and consider the equation Ax = c, with c = [1 0 − 1 ]T . Suppose that the two vectors x1 =[ 1 2 3]T and x2 =[ 3 2 1] T are solutions to the above equation.

(a) Find a vector v in N (A).

(b) Using the result in part (a), find another solution to the equation Ax = c.

(c) With the given information, what are the possible values for null(A)?

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