Solve the following systems of linear equations by Gaussian elimination method.
Problem 1 :
2x - 2y + 3z = 2, x + 2y - z = 3 and 3x - y + 2z = 1
Problem 2 :
2x + 4y + 6z = 22, 3z + 8y + 5z = 27, -x + y + 2z = 2
Problem 3 :
If ax^{2}+bx+c is divided by x + 3, x - 5 and x - 1, the remainders are 21, 61 and 9. Find a, b and c.(Use Gaussian elimination method)
Problem 4 :
An amount of 65000 is invested in three bonds at the rates of 6%, 8% and 9% per annum respectively. The total income is 4800. The income from the third bond is 600 more than that from the second bond. Determine the price of each bond.
Problem 5 :
A boy is walking along the path y = ax^{2} + bx + c through the points (-6, 8), (-2, -12) and (3, 8). He wants to meet his friend at P (7, 60) . Will he meet his friend? (Use Gaussian elimination method.)
1) (-1, 4, 4)
2) (3, 1, 2)
3) (2, 1, 6)
4) x = 30000, y = 15000, z = 20000
5) a = 1, b = 3 and c = -10
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM