
Understanding Linear Transformations in Polynomial Vector Spaces

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
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 standard basis vector for the polynomial x in the vector space of second-degree polynomials?
[1, 0, 0]
[1, 1, 0]
[0, 0, 1]
[0, 1, 0]
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the function f(p(x)) = p(x + 4) represent in the context of polynomial vector spaces?
A matrix inversion
A polynomial division
A linear transformation
A quadratic equation
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the transformation matrix determined for the function f(p(x)) = p(x + 4)?
By using polynomial long division
By determining the transformations of the standard basis vectors
By evaluating the function at x = 0
By solving a quadratic equation
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first column of the transformation matrix when p(x) = 1?
[1, 0, 0]
[1, 1, 1]
[0, 1, 0]
[0, 0, 1]
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When p(x) = x, what is the resulting vector after applying the transformation f(p(x)) = p(x + 4)?
[0, 1, 4]
[4, 0, 1]
[4, 1, 0]
[1, 4, 0]
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the third column of the transformation matrix when p(x) = x^2?
[16, 1, 8]
[1, 8, 16]
[16, 8, 1]
[8, 16, 1]
Tags
CCSS.HSN.VM.A.1
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the polynomial 8 + 2x + 7x^2 represented as a vector?
[2, 8, 7]
[8, 7, 2]
[7, 2, 8]
[8, 2, 7]
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