Elementary Row Operations and Systems

Elementary Row Operations and Systems

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial explores two special cases in solving systems of equations: inconsistency and redundancy. It demonstrates how to set up augmented matrices and use elementary row operations to identify these cases. An inconsistent system results in no solutions, while a redundant system leads to infinite solutions. The tutorial provides step-by-step examples to illustrate these concepts.

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18 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the two special cases to consider when solving a system of equations?

Consistency and uniqueness

Redundancy and singularity

Inconsistency and dependency

Inconsistency and redundancy

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in solving the system of equations X - 2y + 3z = 1, -X + 3y - 2z = -1, and 2X - 4y + 6z = 5?

Graphing the equations

Substituting values

Finding the determinant

Setting up the augmented matrix

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of using elementary row operations on the augmented matrix?

To eliminate variables

To graph the equations

To achieve an upper triangular matrix

To find the determinant

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of adding Row 1 to Row 2 in the first system?

0 1 1 0

1 0 0 1

1 1 0 0

0 0 1 1

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of subtracting 2 times Row 1 from Row 3 in the first system?

0 0 0 3

1 1 1 1

2 2 2 2

0 0 0 0

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does a row of zeros with a non-zero constant in the augmented matrix indicate?

The system is redundant

The system has infinite solutions

The system has a unique solution

The system is inconsistent

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in setting up the augmented matrix for the second system of equations?

Using the coefficients of x, y, and z

Finding the inverse of the matrix

Substituting known values

Graphing the equations

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