An overdetermined homogeneous system of linear equations.

Step 2

The homogeneous system of linear equations is said to be overdetermined if the number of equations m is more than the number of unknowns n.

If all the equations are linearly independent and m >n then there is no solution.

Step 3

If the system of equation is consistent, then, in this case, there is either one solution or set of solutions.

If all the equations are not linearly independent and s out of m equations are linearly independent, and if

(i) s>n, then there is no solution.

(ii) If s=n, then the system has either one solution or no solution.

(iii) If s For example:

Consider the homogeneous system of linear equations.

x+y=0, 2x+3y=0, 3x+2y=0

Here the number of equations is m=3 and the number of unknowns n=2.

As m>n, therefore, the system is overdetermined.

x=y=0 satisfy the equations.

Step 2

The homogeneous system of linear equations is said to be overdetermined if the number of equations m is more than the number of unknowns n.

If all the equations are linearly independent and m >n then there is no solution.

Step 3

If the system of equation is consistent, then, in this case, there is either one solution or set of solutions.

If all the equations are not linearly independent and s out of m equations are linearly independent, and if

(i) s>n, then there is no solution.

(ii) If s=n, then the system has either one solution or no solution.

(iii) If s For example:

Consider the homogeneous system of linear equations.

x+y=0, 2x+3y=0, 3x+2y=0

Here the number of equations is m=3 and the number of unknowns n=2.

As m>n, therefore, the system is overdetermined.

x=y=0 satisfy the equations.