Evaluate the determinants in Exercises 1 and 2. 1. 2 4 5 1 2. (i) cos sin sin cos q q q q (ii) 2 1 1 1 1 x x x x x + + + 3. If A = 1 2 4 2 , then show that | 2A | = 4 | A | 4. If A = 1 0 1 0 1 2 0 0 4 , then show that | 3 A | = 27 | A | 5. Evaluate the determinants (i) 3 1 2 0 0 1 3 5 0 (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 3 5 0 6. If A = 1 1 2 2 1 3 5 4 9 , find | A | 7. 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 = 8. If 2 6 2 18 18 6 x x = , then x is equal to (A) 6 (B) 6 (C) 6 (D) 0
Question 1:2 4 –5 –1
Question 2:(i) cos – sin sin cos q q q q (ii) 2 – 1 – 1 1 1 x x x x x + + +
Question 3:If A = 1 2 4 2 , then show that | 2A | = 4 | A |
Question 4:If A = 1 0 1 0 1 2 0 0 4 , then show that | 3 A | = 27 | A |
Question 5:Evaluate the determinants (i) 3 –1 –2 0 0 –1 3 –5 0 (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 3 –5 0
Question 6:If A = 1 1 –2 2 1 –3 5 4 –9 , find | A |
Question 7: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 =
Question 8:If 2 6 2 18 18 6 x x = , then x is equal to (A) 6 (B) ± 6 (C) – 6 (D) 0