Algebra 58 - Gauss-Jordan Elimination with Dependent Systems

Algebra 58 - Gauss-Jordan Elimination with Dependent Systems

Assessment

Interactive Video

Mathematics

11th Grade - University

Hard

Created by

Quizizz Content

FREE Resource

The video tutorial explains how to identify dependent systems of linear equations and demonstrates the use of Gauss-Jordan elimination to simplify these systems. Through examples, it shows how dependent equations can be transformed into independent systems with fewer equations, making it easier to determine solution sets. The tutorial covers cases where equations are multiples of each other and where they are linear combinations, highlighting the process of converting matrices to reduced row echelon form.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a dependent system of linear equations?

A system with exactly one solution

A system where some equations are dependent on others

A system with no solutions

A system where equations are independent

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How does Gauss-Jordan elimination help with dependent systems?

It provides a graphical solution

It only works for independent systems

It adds more equations to the system

It identifies dependent equations and simplifies the system

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the first example, what indicates that the system is dependent?

The equations have different variables

The second equation is a multiple of the first

The equations have no solutions

The equations are in reduced row echelon form

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What happens to the second row during Gauss-Jordan elimination in the first example?

It remains unchanged

It becomes a row of all zeros

It becomes the first row

It is removed from the matrix

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the second example, what is unique about the system of equations?

The equations are in different dimensions

All equations are independent

All equations are multiples of each other

The system has no solutions

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of Gauss-Jordan elimination in the second example?

A system with more variables

Three independent equations

A single equation representing the solution set

A system with no solutions

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the third example, how are the equations related?

Each equation is a linear combination of the other two

All equations are independent

The equations have no common solution

Each equation is a multiple of the first

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