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Problem 6: Let \( m>n \) be two positive integers, Which of the following statements are always tr ...
Problem 6: Let \( m>n \) be two positive integers, Which of the following statements are always true? (i) Any linear system of \( n \) equations in \( m \) variables is consistent. (ii) Any linear system of \( m \) equations in \( n \) variables is consistent. (iii) Any homogeneous linear system of \( n \) equations in \( m \) variables has infinitely many solutions. (iv) Any homogeneous linear system of \( m \) equations in \( n \) variables has infinitely many solutions. A. (i) and (iii) only. B. (ii) and (iv) only C. (i), (ii), (iii) and (iv). D. (i) only. E. (iii) only.