Question

The augmented matrix of a consistent system of five equa- tions in seven unknowns has rank equal to three. How many parameters are needed to specify all solutions?

Answer 1

4 parameters are necessary to specify all solutions and correspond to the number of free variables of the system.

Explanation:

Remember that the number of free variables of a system is equal to m-rank(A) where m is the number of unknowns variables and A is the matrix of the system.

Since the system is consistent and the rank of the matrix is 3 then echelon form of the augmented matrix has two rows of zeros.

Then m-rank(A)=7-3=4.