
Understanding Transition Matrices and Bases

Interactive Video
•
Mathematics
•
9th - 10th Grade
•
Hard

Olivia Brooks
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is changing from one basis to another useful?
It helps express problems in a more solvable form.
It makes problems more complex.
It is only useful in three-dimensional spaces.
It changes the vector itself.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the simplest basis in the vector space R2?
Unit vectors in the x and y directions.
Vectors of length two in x and y directions.
Vectors of length one in the z direction.
Any two non-parallel vectors.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How can a vector in R2 be expressed in terms of a basis?
As a single scalar value.
As a product of its coordinates.
As a linear combination of basis vectors.
As a sum of its coordinates.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does a transition matrix do?
It is used to find the length of a vector.
It only works in three-dimensional spaces.
It relates coefficients in different bases.
It changes the vector itself.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the role of the inverse of a transition matrix?
It is not used in basis transformation.
It changes the vector's direction.
It is used to isolate the new coordinates.
It is used to find the original vector.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you find the inverse of a 2x2 matrix?
By subtracting the diagonal terms.
By multiplying all terms by two.
By switching diagonal terms and changing signs of others, then dividing by the determinant.
By adding the diagonal terms.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the determinant of the transition matrix U in the example?
Zero
Negative three
Three
One
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