
Understanding Orthogonal Matrices and Transformations

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

Aiden Montgomery
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a key characteristic of an orthogonal matrix?
Its columns are not linearly independent.
Its determinant is always zero.
It has no inverse.
Its transpose is equal to its inverse.
Tags
CCSS.HSN.VM.A.1
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How does an orthogonal matrix relate to a change of basis?
It changes the vector's magnitude.
It alters the vector's direction.
It represents the same vector in a different coordinate system.
It distorts the vector's shape.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does an orthogonal matrix preserve when applied to a vector?
Neither the vector's length nor angle.
Only the vector's angle.
Only the vector's length.
Both the vector's length and angle.
Tags
CCSS.HSN.VM.C.11
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens to a vector's length when multiplied by an orthogonal matrix?
It doubles.
It becomes zero.
It remains unchanged.
It halves.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the length of a vector defined in terms of dot products?
As the sum of its components.
As the square root of the dot product with itself.
As the product of its components.
As the inverse of its dot product.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the relationship between the dot product and the angle between two vectors?
The dot product is the product of the vectors' lengths times the cosine of the angle.
The dot product is always zero.
The dot product is the sum of the vectors' lengths.
The dot product is the product of the vectors' lengths times the sine of the angle.
Tags
CCSS.HSN.VM.C.10
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the identity matrix represent in the context of orthogonal matrices?
A matrix with all zero entries.
A matrix that doubles the vector's length.
A matrix that changes the vector's direction.
A matrix that does not alter the vector.
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