The augmented matrix of a consistent system of five equa- tions in seven unknowns has rank equal to three. How many parameters a

Question

LuckyWell [14K]

3 years ago

8

The augmented matrix of a consistent system of five equa- tions in seven unknowns has rank equal to three. How many parameters a

re needed to specify all solutions?

Mathematics

1 answer:

ale4655 [162] · Answer 1 · 2022-01-24T22:39:03+03:00

Answer:

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

Step-by-step 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.