MTH501 Linear Algebra Assignment No.1 Solution Spring Semester 2013 Due Date:07-05-20

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MTH501 Linear Algebra Assignment No.1 Solution Spring Semester 2013 Due Date:07-05-2013


Question: 1 Marks: 30
Analyze the following critical but interesting things using the following system of linear equations:
Using the following system of linear equations:

1) State the reason why the consistency and inconsistency of the given system is depending on its coefficient matrix. The reason should be very clear.

2) Determine the value of ‘’ that makes the given system inconsistent. Also, what will be the value of the determinant corresponding to that value of?

3) Determine the values of those makes the above system consistent. Also, calculate the determinant corresponding to those values of?

4) Determine the values of the unknowns in the given system corresponding to and.

5) Determine the free variable from the above system of equations.

6) Also discuss the uniqueness and non-uniqueness of the solution of the given system. I mean to say that is it possible for a system to have a unique solution? If it has then what will be the conditions on the system if not then what will be the conditions.

Note:

The value of the determinant plays a vital role in determining the consistency and inconsistency, so to solve (1) think about the nature of the determinant.
You can calculate the value of using Gauss Jordan technique and also by computing directly the determinant of the coefficient matrix. Then putting the value of in the above system, the determinant can be calculated in (2).
(3) Can be solved using Gauss Jordan technique, I mean reduced echelon form will tell you about the required values.

Note:

I am not demanding the correct solution of the given question. I have a desire that you should learn something that is why I am giving such kind of the problem. Please attempt it and do not believe on cheating. I promise to all of you, the person whose attempt will be real and genuine would be awarded good marks and the person whose attempt will not be genuine, would be awarded zero marks. You can discuss the problems with me related to the assignment through email. I will provide to all of you the maximum assistance to remove the difficulties but do not demand the whole solution from my side. Some hints have been provided above. Please read them carefully and attempt the assignment honestly. Take care all of you and good luck. Allah Hafiz. Thanks for reading the footnotes.