Dependent system
from class: 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.
congrats on reading the definition of dependent system . now let's actually learn it.
Predict what's on your test 5 Must Know Facts For Your Next Test When graphed, the lines in a dependent system overlap completely. A dependent system has infinitely many solutions because any point on the line satisfies all equations. The determinant of the coefficient matrix for a dependent system is zero. In reduced row-echelon form, a dependent system will have at least one row of all zeros. 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? "Dependent system" also found in:
© 2024 Fiveable Inc. All rights reserved. AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.