EXERCISE 1.5
1. Solve the following systems
of linear equations
by Gaussian elimination method:
(i) 2x - 2 y + 3z = 2, x + 2 y -
z
= 3, 3x - y + 2z
= 1
(ii) 2x + 4 y + 6z = 22, 3x + 8 y + 5z = 27, -
x + y + 2z = 2
2. If
ax2
+ bx + c is
divided by x +
3, x - 5 , and x -1,
the remainders are 21, 61 and
9 respectively. Find a, b and c. (Use Gaussian elimination method.)
3. An amount of ₹ 65,000 is invested in three bonds at the
rates of 6%, 8% and 10% per annum
respectively. The total annual income is ₹ 4,800. The income from the third
bond is ₹ 600 more than that from the second bond. Determine the price of each
bond. (Use Gaussian elimination method.)
4. A boy is walking along the path y = ax2
+ 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.)
Answers for Exercise 1.5:
1. (i) x = -1, y = 4, z = 4
(ii) x = 3, y = 1, z = 2
2. a = 2, b = 1, c = 6
3. ₹ 30000, ₹ 15000, ₹ 20000
4. a = 1, b = 3, c = -10 , yes
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