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(a) Solve the following linear systems by the process of elimination : 3 x + 2y + 5z = 9 x — y + $z = 2 3x — 6y z = 26 (b) Give an example, with justification, of each of the following : 2 (i) An element of (C x Q) \(Q x C); (ii) An infinite set whose complement in R is infinite. 2. (a) Find the roots of the polynomial equation x4— 9x3+ 17x2+ 33x — 90 = 0, given that two of its roots are equal to 3. 2 (b) Use the principle of mathematical induction to show that for any positive integer n, (311— 2n) > O. 3. (a) A coach buys 3 cricket bats and 6 balls for 3,900. Later, he buys 1 bat and 3 balls for another team for 1,450. Write two linear equations to represent the purchases. Why can the linear system so obtained be solved by Cramer's rule ? Also, use the rule to solve the system, and interpret the solution in the given context. 4 (b) Give an example of a 4 x 1 matrix with entries from Z \ N. 1
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