
Understanding Linear Independence and Null Space

Interactive Video
•
Mathematics
•
11th Grade - University
•
Hard
Standards-aligned

Emma Peterson
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the definition of an M by N matrix?
A matrix with M columns and N rows
A matrix with equal number of rows and columns
A matrix with M rows and N columns
A matrix with N rows and M columns
Tags
CCSS.HSN.VM.C.8
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How can each column of a matrix be viewed?
As an M-dimensional vector
As a scalar
As a row vector
As a single number
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the null space of a matrix?
The set of all vectors that result in a zero vector when multiplied by the matrix
The set of all vectors that result in a non-zero vector when multiplied by the matrix
The set of all zero vectors
The set of all vectors with non-zero components
Tags
CCSS.HSN.VM.C.8
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why must a vector X be a member of RN for matrix multiplication to work?
Because it ensures the vector has equal components
Because it ensures the vector has zero components
Because it ensures the vector has N components
Because it ensures the vector has M components
Tags
CCSS.HSN.VM.C.11
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of multiplying a matrix by a vector in its null space?
A scalar
A zero vector
A non-zero vector
Another matrix
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What condition must be met for vectors to be linearly independent?
They must be orthogonal
The only solution to their linear combination being zero is if all coefficients are zero
They can be expressed as a linear combination of each other
They must have the same number of components
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does it mean if the null space of a matrix only contains the zero vector?
The matrix is singular
The matrix is invertible
The column vectors of the matrix are linearly independent
The column vectors of the matrix are linearly dependent
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