Which of the following statements are TRUE: (1) A system of 3 linear equations in 3 variables always has a unique solution. (2) There is no system of linear equations which has exactly 3 solutions. (3) A system of 3 linear equations in 4 variables never has a unique solution. O (1) and (3) None of the others are correct (3) only O (1) only O (2) only (2) and (3)

For an n xn system of linear equations, which of the following statement can never be true? (a) There is no solution (b) There is exactly one solution (c) There are exactly two solutions (d) There are infinitely many solutions

7. Consider the following system of linear equations: X1-X2 + 2x3 = 1 -X1 + x3 = 41+s (-2x1+x2+ rx3 = 2 1) For what values of r and s is this system of linear equations inconsistent? 2) For what values of r and s is this system of linear equations have infinitely many solutions? 3) For what values of r and s is this system of linear equations have a unique solution?

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