
Understanding the Null Space of a Matrix

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard

Aiden Montgomery
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the null space of a matrix A?
The set of all vectors x such that Ax equals the identity matrix.
The set of all vectors x such that Ax equals a scalar multiple of x.
The set of all vectors x such that Ax equals the zero vector.
The set of all vectors x such that Ax equals a non-zero vector.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following is NOT a subspace axiom?
The subset is closed under addition.
The zero vector is in the subset.
The subset is closed under matrix multiplication.
The subset is closed under scalar multiplication.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is the zero vector included in the null space of a matrix?
Because it is the only vector that satisfies Ax = 0.
Because Ax = 0 for the zero vector.
Because it is a requirement of matrix multiplication.
Because it is a requirement of vector addition.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If vectors u and v are in the null space of A, what can be said about their sum?
The sum is equal to the zero vector.
The sum is in the null space of A.
The sum is equal to a scalar multiple of u.
The sum is not in the null space of A.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does it mean for a subset to be closed under scalar multiplication?
Only zero multiples of a vector in the subset are in the subset.
Only integer multiples of a vector in the subset are in the subset.
Any scalar multiple of a vector in the subset is not in the subset.
Any scalar multiple of a vector in the subset is also in the subset.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
If a vector u is in the null space of A, what can be said about c*u for any real number c?
c*u is equal to a scalar multiple of v.
c*u is equal to the zero vector.
c*u is in the null space of A.
c*u is not in the null space of A.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of multiplying a zero vector by any scalar?
A vector equal to the scalar.
A vector equal to the identity matrix.
A non-zero vector.
The zero vector.
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