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Dependent system

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College Algebra

Definition

A dependent system is a system of linear equations in which all equations represent the same line, resulting in infinitely many solutions. This occurs when the equations are scalar multiples of one another.

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5 Must Know Facts For Your Next Test

  1. When graphed, the lines in a dependent system overlap completely.
  2. A dependent system has infinitely many solutions because any point on the line satisfies all equations.
  3. The determinant of the coefficient matrix for a dependent system is zero.
  4. In reduced row-echelon form, a dependent system will have at least one row of all zeros.
  5. A consistent and dependent system implies that there is no unique solution.

Review Questions

  • What does it mean for a system of linear equations to be dependent?
  • How can you identify a dependent system from its graph?
  • What is the significance of having a row of all zeros in reduced row-echelon form?

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