Page:Elementary algebra (1896).djvu/467

449 Rh = 3 8 20 5 15 36 9 7 17 4 = 3 8 20 5 8 19 5 7 17 4 = 3 0 1 0 8 19 5 7 17 4 = -3 8 5 7 4 =0

EXAMPLES XLVII. b.

Calculate the values of the determinants

1. 1 1 1 1 1 2 3 4 1 3 6 10 1 4 10 20

2. 7 13 10 6 5 9 7 4 8 12 11 7 4 10 6 3

3. a 1 1 1 1 a 1 1 1 1 a 1 1 1 1 a

4. 0 1 1 1 1 b+c a a 1 b c+a b 1 c c a+b

5. 3 2 1 4 15 29 2 14 16 19 3 17 33 39 8 38

6. 1+a 1 1 1 1 1+b 1 1 1 1 1+c 1 1 1 1 1+d

7. 0 x y z x 0 z y y z 0 x z y x 0

8. 0 x y z -x 0 c b -y -c 0 a -z -b -a 0

Solve the equations:

9. 4x - 5y + 2z = 11, 2x + 3y- z = 20, 7x-4y + 3z = 33.

10. x 2 + y 3 + z 4 = 7 x + 2y + 3z = 48, x 3 - 2y 3 + z 3 = 4

11. 2x - y + 3z - 2u = 14, x + 7y + 2z - u = 13, 3x + 5y - 5z + 3u = 11, 4x-3y + 2z- u = 21.

12. x+ y+ z = l, ax + by + Cz = k, a^2x + y^2y + c^2z = k^2.

13. ax + by + cz = k, a^2x + b^2y + c^2z = k^2, a^3x + b^3y + cz = k^3.

14. x+ y + z + u = 1, ax + by + cz + du = k, a^2x + b^2y + c^2z + d^2u = k^2, a^3x + b^3y + c^3z + d^3u = k^3.