
Understanding Column Space of a Matrix

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

Liam Anderson
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the column space of a matrix?
The set of all possible row combinations
The span of the matrix's columns
The determinant of the matrix
The inverse of the matrix
Tags
CCSS.HSN.VM.C.6
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example of a 3x4 matrix, how many components do the column vectors have?
5 components
2 components
3 components
4 components
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When does the column space of a matrix span all of R^m?
When the matrix is square
When there is a pivot in each row
When the determinant is zero
When the matrix is diagonal
Tags
CCSS.8.EE.C.8B
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step to check if a vector is in the column space of a matrix?
Calculate the determinant
Find the inverse of the matrix
Solve the equation A * x = v
Perform row operations
Tags
CCSS.8.EE.C.8B
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does a row of zeros in the reduced row echelon form indicate?
No solution exists
A unique solution exists
An infinite number of solutions exist
The matrix is singular
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result if there is a contradiction in the row operations?
The vector is in the column space
The vector is not in the column space
The matrix is invertible
The matrix is singular
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does it mean if a vector equation has at least one solution?
The vector is not in the column space
The matrix is diagonal
The matrix is singular
The vector is in the column space
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