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Problem Questions with Answer, Solution - Exercise 1.5: Matrix: Gaussian Elimination Method | 12th Mathematics : UNIT 1 : Applications of Matrices and Determinants

Chapter: 12th Mathematics : UNIT 1 : Applications of Matrices and Determinants

Exercise 1.5: Matrix: Gaussian Elimination Method

Solve the following systems of linear equations by Gaussian elimination method:

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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12th Mathematics : UNIT 1 : Applications of Matrices and Determinants : Exercise 1.5: Matrix: Gaussian Elimination Method | Problem Questions with Answer, Solution

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12th Mathematics : UNIT 1 : Applications of Matrices and Determinants


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