Change of Basis
Interactive Video
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Mathematics
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11th Grade - University
•
Hard
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7 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the simplest basis for the vector space R2?
Any two non-parallel vectors
Unit vectors in the X and Y directions
Vectors of any length in the X and Y directions
Vectors in the Z direction
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When changing the basis of a vector, what remains unchanged?
The dimensionality of the space
The vector itself
The coordinates of the vector
The basis vectors
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the role of a transition matrix?
To change the vector itself
To increase the dimensionality of the space
To relate coefficients between different bases
To eliminate the need for basis vectors
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the transition matrix consist of?
The inverse of the original matrix
The new basis vectors as columns
The original vector components
The identity matrix
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you find the inverse of a 2x2 matrix?
Multiply all terms by -1
Add the identity matrix
Switch the diagonal terms and flip the sign of the other terms, then divide by the determinant
Transpose the matrix
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a key property of matrix multiplication that must be considered?
It is not commutative
It is commutative
It is associative
It is distributive
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of using inverse matrices in changing bases?
To find the original vector
To increase the vector's magnitude
To isolate the new coordinates
To eliminate the need for a transition matrix
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