The augmented matrix of a consistent system of five equations in seven unknowns has rank equal to...

Question:

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

Consistent System:

A system is consistent when the range of an array and the augmented augmented are equal.

If they are equal but at an amount less than the number of unknowns, the number of system solutions is infinite.

Answer and Explanation:

Taking into account that the number of parameters that form the solution of a consistent system is equal to the number of variables minus the range of the matrices of the system and the augmented matrix (both ranges are equal):

In this case, the number of independent parameters is: 5-3 = 2.


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Inconsistent System of Equations: Definition & Example

from High School Algebra II: Homework Help Resource

Chapter 8 / Lesson 9
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