
Understanding Echelon Form, Pivots, and Free Variables

Interactive Video
•
Mathematics
•
9th - 12th Grade
•
Hard
Standards-aligned

Olivia Brooks
FREE Resource
Standards-aligned
Read more
10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the primary goal of the video tutorial?
To solve complex equations
To define Echelon form, pivots, and free variables
To learn about matrix multiplication
To understand linear transformations
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which condition is NOT required for a matrix to be in Echelon form?
Nonzero entries form a triangle in the lower left corner
All elements below a leading coefficient are zero
Leading nonzero entries are to the left of zero entries
All zero rows are at the bottom
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What are pivots in a matrix?
The last nonzero elements in each row
The diagonal elements of the matrix
The first nonzero elements in each row
The zero elements in each row
Tags
CCSS.8.EE.C.8B
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How many free variables are there if the number of equations equals the number of variables?
Zero
One
Infinite
Two
Tags
CCSS.8.EE.C.8B
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens when the number of variables exceeds the number of equations in a system?
The system is inconsistent
There are infinite solutions
There is a unique solution
There are no solutions
Tags
CCSS.8.EE.C.8B
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the first example, how many free variables are there?
Two
Three
One
Zero
Tags
CCSS.8.EE.C.8B
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the second example, how many free variables are present?
Zero
One
Two
Three
Tags
CCSS.8.EE.C.8B
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