Problem Questions with Answer, Solution - Exercise 1.4: Matrices: Cramer’s Rule | 12th Mathematics : UNIT 1 : Applications of Matrices and Determinants
Chapter: 12th Mathematics : UNIT 1 : Applications of Matrices and Determinants
Exercise 1.4: Matrices: Cramer’s Rule
Maths Book back answers and solution for Exercise questions - Solve the following systems of linear equations by Cramer’s rule
EXERCISE 1.4
1. Solve the following systems of linear equations by Cramer’s rule:
(i) 5x - 2 y +16 = 0, x + 3y - 7 = 0
2. In a competitive examination, one mark is awarded for every correct answer while ¼ mark is deducted for every wrong answer. A student answered 100 questions and got 80 marks. How many questions did he answer correctly ? (Use Cramer’s rule to solve the problem).
3. A chemist has one solution which is 50% acid and another solution which is 25% acid. How much each should be mixed to make 10 litres of a 40% acid solution ? (Use Cramer’s rule to solve the problem).
4. A fish tank can be filled in 10 minutes using both pumps A and B simultaneously. However, pump B can pump water in or out at the same rate. If pump B is inadvertently run in reverse, then the tank will be filled in 30 minutes. How long would it take each pump to fill the tank by itself ? (Use Cramer’s rule to solve the problem).
5. A family of 3 people went out for dinner in a restaurant. The cost of two dosai, three idlies and two vadais is ₹ 150. The cost of the two dosai, two idlies and four vadais is ₹ 200. The cost of five dosai, four idlies and two vadais is ₹ 250. The family has ₹ 350 in hand and they ate 3 dosai and six idlies and six vadais. Will they be able to manage to pay the bill within the amount they had ?
Answers for Exercise 1.4:
1. (i) x = -2, y = 3
(ii) x = 1/2 , y = 3
(iii) x = 2, y = 3, z = 4
(iv) x = 1, y = 3, z = 3
2. 84
3. 50% acid is 6 litres, 25% acid is 4 litres
4. Pump A : 15 minutes, Pump B : 30 minutes
5. ₹ 30/-, ₹ 10/-, ₹ 30/-, yes
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12th Mathematics : UNIT 1 : Applications of Matrices and Determinants : Exercise 1.4: Matrices: Cramer’s Rule | Problem Questions with Answer, Solution
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12th Mathematics : UNIT 1 : Applications of Matrices and Determinants