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?

Question

Tequila

Mathematics

23 December, 23:35

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?

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Answers (1)

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Jamar Stuart · Answer 1

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.