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# Miscellaneous problems

Business Maths and Statistics : Applications of Matrices and Determinants: Miscellaneous problems with Answers, Solution and Explanation

Miscellaneous problems

1. Find the rank of the matrix  2. Find the rank of the matrix A =  3. Find the rank of the matrix A =  4. Examine the consistency of the system of equations: x y + z = 7 , x + 2 y + 3z = 18, y + 2z = 6 . 5. Find k if the equations 2x + 3y ŌłÆ z = 5 , 3x ŌłÆ y + 4z = 2 , x + 7 y ŌłÆ 6z = k are consistent. 6. Find k if the equations x + y + z = 1, 3x ŌłÆ y ŌłÆ z = 4, x + 5y + 5z = k are inconsistent.

1. 7. Solve the equations x + 2 y + z = 7, 2x ŌłÆ y + 2z = 4, x + y ŌłÆ 2z = ŌłÆ1 by using CramerŌĆÖs rule 8. The cost of 2kg. of wheat and 1kg. of sugar is Ōé╣100. The cost of 1kg. of wheat and 1kg. of rice is Ōé╣80. The cost of 3kg. of wheat, 2kg. of sugar and 1kg of rice is Ōé╣220. Find the cost of each per kg., using CramerŌĆÖs rule. 9. A salesman has the following record of sales during three months for three items A,B and C, which have different rates of commission. Find out the rate of commission on the items A,B and C by using CramerŌĆÖs rule.  10. The subscription department of a magazine sends out a letter to a large mailing list inviting subscriptions for the magazine. Some of the people receiving this letter already subscribe to the magazine while others do not. From this mailing list, 60% of those who already subscribe will subscribe again while 25% of those who do not now subscribe will subscribe. On the last letter it was found that 40% of those receiving it ordered a subscription. What percent of those receiving the current letter can be expected to order a subscription? 1. Žü(A)= 2

2. Žü(A) = 3

3. Žü(A) = 3

4. The given system is inconsistent and has no solution.

5. k = 8.

6. The equations are inconsistent when k assumes any real value other than 0.

7. x=1,  y = 2 , and z = 2

8. Cost of wheat is Ōé╣30/kg, Cost of sugar is Ōé╣40/kg and Cost of rice is Ōé╣50/kg.

9. The rates of commission for A,B and C are Ōé╣2, Ōé╣4 and Ōé╣11 respectively

10. 39%

Tags : Applications of Matrices and Determinants , 12th Business Maths and Statistics : Chapter 1 : Applications of Matrices and Determinants
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12th Business Maths and Statistics : Chapter 1 : Applications of Matrices and Determinants : Miscellaneous problems | Applications of Matrices and Determinants