
Understanding Linear Transformations and Eigenvectors

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

Sophia Harris
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of applying a linear transformation to a vector using a matrix?
The vector is scaled and possibly rotated.
The vector is translated.
The vector remains unchanged.
The vector is rotated.
Tags
CCSS.HSN.VM.A.1
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following is true about eigenvectors?
They are vectors that always have a magnitude of one.
They are vectors that always lie on the x-axis.
They are vectors that do not change direction under a transformation.
They are always perpendicular to each other.
Tags
CCSS.HSN.VM.A.1
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the eigenvalue associated with the vector (2, 2)?
1
2
0
3
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the eigenvalue associated with the vector (-3, 3)?
2
0
1
3
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens to the vector (2, 2) under the given transformation?
It is scaled by a factor of 1.
It remains unchanged.
It is scaled by a factor of 3.
It is rotated by 90 degrees.
Tags
CCSS.HSN.VM.C.11
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How does the vector (-3, 3) transform under the given matrix?
It is scaled by a factor of 3.
It is scaled by a factor of 0.
It remains unchanged.
It is scaled by a factor of 2.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the effect of the transformation on the unit circle along the line y = x?
It is stretched by a factor of 3.
It is compressed by a factor of 3.
It is rotated by 45 degrees.
It remains unchanged.
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