# MTH501 Linear Algebra Assignment 1 Solution Spring 2013

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.