Exercise 4.1

(i) / cos - sin / sin cos / θ θ / θ θ (ii) 2 - 1 - 1 1 1

x x / + / + +

If A = 1 2 4 2      , then show that | 2A | = 4 | A |

If A = 1 0 1 0 1 2 0 0 4          , then show that | 3 A | = 27 | A |

Evaluate the determinants (i) 3 -1 -2 / 0 0 -1

(ii) 3 - 4 5 / 1 1 -2 / 2 3 1 (iii) 0 1 2 / -1 0 -3 / -2 3 0 (iv) 2 -1 -2 / 0 2 -1

If A = 1 1 -2 2 1 -3 5 4 -9          , find | A |

Find values of x, if (i) 2 4 2 4 / 5 1 6 / x / x= (ii) 2 3 3 / 4 5 2 5 / x x=

18 18 6 / x x = , then x is equal to (A) 6 (B) ± 6 (C) - 6 (D) 0