(a) Let C be a matrix with full column rank. Show that the solution of any compatible

system Cx = d is unique.

(b) Use part (a) and the decomposition of Exercise 3.3 to show that if A be an m n

matrix with rank m, then the system Ax = b is compatible for every b 2 Rm.

(c) Construct a 24 matrix A and a 21 right-hand side vector b to show that the result

of part (b) does not hold if A is not of full rank.

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