Answer to Question #98543 in Algebra for Shaheli Chattopadhyay

Question

(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

Answer 1

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