Page:Elementary algebra (1896).djvu/461

443 Rh EXAMPLES XLVII. a.

Calculate the values of the determinants : 1. 1 1 1 35 37 34 23 26 25

2. 13 16 19 14 17 20 15 18 21

3. 13 3 23 . 30 7 53 39 9 70

4. a h g h b f 9 f c

5. 1 z -y - z 1 x y -x 1

6. 1 1 1 1 1+x 1 1 1 1+y

7. a-b b-c c-a b-c c-a a-b c-a a-b b-c

8. b+c a a b c+a b c c a+ b 9. Without expanding the determinants, prove that

a b c x y z p q r y b q  x a p z c r

x y z p q r a b c

Solve the equations

10. a a x m m m h x b

11. 15-2x 11 10 11-3x 17 16 7-x 14 13

Prove the following identities

12. b+c c+a a+b q+r r+p p+q y+z z+x x+y = 2 a b c p q r x y z

13. 1 a a^2 1 b b^2 1 c c^2 = (b-c)(c-a)(a-b).

14. 1 1 1 a b c a^3 b^3 c^3 = (b - c){c. - a)(a - b)(a + b + c).

Calculate the value of the determinants :

15. 3 6 9 4 7 10 5 8 11

16. 1 1 1 x y z x^2 y^2 z^2