Book back answers and solution for Exercise questions - Business Maths and Statistics : Applications of Matrices and Determinants: Solved Example Problems

Exercise 1.1

1. Find the rank of each of the following matrices

2. If A = and B = , then find the rank of AB and the rank of BA.

3. Solve the following system of equations by rank method

*x *+* y *+* z *=* *9, 2*x *+* *5*y *+* *7*z *=* *52, 2*x* âˆ’ *y* âˆ’ *z* = 0

4. Show that the equations 5*x* + 3*y* + 7*z* = 4, 3*x* + 26 *y* + 2*z* = 9, 7*x* + 2 *y* + 10*z* = 5 are consistent and solve them by rank method.

5. Show that the following system of equations have unique solution:

*x *+* y *+* z *=* *3,* x *+* *2* y *+* *3*z *=* *4,* x *+* *4* y *+* *9*z *=* *6* *by rank method.

6. For what values of the parameter *Î»* , will the following equations fail to have unique solution: 3*x* âˆ’ *y* + *Î»** z* = 1, 2*x* + *y* + *z* = 2, *x* + 2 *y* âˆ’ *Î»** z* = âˆ’1 by rank method.

7. The price of three commodities *X,Y* and *Z* are *x,y* and *z* respectively Mr.Anand purchases 6 units of *Z* and sells 2 units of *X* and 3 units of Y. Mr.Amar purchases a unit of *Y* and sells 3 units of *X* and 2units of *Z*. Mr.Amit purchases a unit of *X* and sells 3 units of *Y* and a unit of *Z*. In the process they earn â‚¹5,000/-, â‚¹2,000/- and â‚¹5,500/- respectively Find the prices per unit of three commodities by rank method.

8. An amount of â‚¹5,000/- is to be deposited in three different bonds bearing 6%, 7% and 8% per year respectively. Total annual income is â‚¹358/-. If the income from first two investments is â‚¹70/- more than the income from the third, then find the amount of investment in each bond by rank method.

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12th Business Maths and Statistics : Chapter 1 : Applications of Matrices and Determinants : Exercise 1.1 : Rank of a Matrix | Problem Questions with Answer, Solution

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