
Understanding Vector Coordinates and Basis Transformation

Interactive Video
•
Mathematics
•
9th - 12th Grade
•
Hard
+1
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 initial problem discussed in the video?
Finding the coordinates of vector x relative to basis B.
Calculating the magnitude of vector x.
Finding the coordinates of vector x relative to the standard basis.
Determining the basis vectors in set B.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which method involves using linear combinations to find vector x's coordinates?
Scalar multiplication
Matrix inversion
Linear combinations
Vector addition
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the first method, what operation is performed with the first basis vector and its coordinate?
Addition
Subtraction
Division
Multiplication
Tags
CCSS.HSN.VM.A.2
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the second method introduced for finding vector x's coordinates?
Using a cross product
Using a transition matrix
Using a determinant
Using a dot product
Tags
CCSS.HSN.VM.A.2
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of the transition matrix in the second method?
To determine the orthogonality of vectors
To transform coordinates from basis B to the standard basis
To find the magnitude of vector x
To calculate the angle between vectors
Tags
CCSS.HSN.VM.A.1
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How are the columns of the transition matrix formed?
Using the standard basis vectors
Using the coordinates of vector x
Using the basis vectors in set B
Using random vectors
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of multiplying the transition matrix by the B coordinates of vector x?
The angle between vector x and the basis vectors
The coordinates of vector x relative to the standard basis
The magnitude of vector x
The orthogonality of vector x
Tags
CCSS.HSN.VM.A.2
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