
Kernel and Image of Transformations

Interactive Video
•
Mathematics
•
11th Grade - University
•
Hard
Standards-aligned

Jackson Turner
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the kernel of a linear transformation?
The set of all output vectors
The set of all input vectors that map to the zero vector
The set of all vectors in the range
The set of all vectors in the domain
Tags
CCSS.HSN.VM.C.10
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the kernel of a transformation related to the null space?
They are unrelated
The kernel is the inverse of the null space
The kernel is equivalent to the null space
The kernel is a subset of the null space
Tags
CCSS.HSN.VM.C.10
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the image of a linear transformation represent?
The set of all vectors in the null space
The set of all input vectors
The set of all output vectors
The set of all vectors in the domain
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the image of a transformation related to the column space?
The image is equivalent to the column space
The image is a subset of the column space
The image is the inverse of the column space
The image is unrelated to the column space
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example, what is the first step to find the kernel of a transformation?
Identify the pivot columns
Determine the free variables
Find the column space
Set up the matrix equation
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does a free variable indicate in the context of finding the kernel?
A unique solution
A vector in the spanning set
A dependent variable
An independent variable
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of parameterizing the solution in the kernel example?
A single vector
A set of vectors
A matrix
A scalar value
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