
Understanding Column Space and Linear Independence

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard
Standards-aligned

Emma Peterson
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in finding the basis for the column space of a matrix?
Identify the non-pivot columns
Find the inverse of the matrix
Convert the matrix to reduced row echelon form
Calculate the determinant
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which columns form the basis for the column space in the given method?
The first, second, and third columns
The second, third, and fourth columns
The first, second, and fourth columns
The first, third, and fifth columns
Tags
CCSS.8.EE.C.8B
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why are the pivot columns in reduced row echelon form linearly independent?
They have unique non-zero entries in each row
They are multiples of each other
They are all zero vectors
They form a square matrix
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What ensures that the solution set of the reduced row echelon form is the same as the original matrix?
The rank of the matrix
The trace of the matrix
The null space of the matrix
The determinant of the matrix
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of the null space in this context?
It shows the linear independence of vectors
It determines the eigenvalues
It is used to calculate the determinant
It helps in finding the inverse
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the only solution to the equation involving linearly independent pivot columns?
Constants are equal to the rank
Constants are equal to the determinant
All constants are zero
All constants are one
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the relationship between the null space of the reduced row echelon form and the original matrix?
One is the inverse of the other
They are equal
They are unrelated
One is the transpose of the other
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