
Linear Independence and Vector Equations
Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Practice Problem
•
Hard
Standards-aligned
Amelia Wright
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the condition for a set of vectors to be linearly independent?
All constants in the vector equation are non-zero.
The vector equation has only the trivial solution.
The vectors form a closed loop.
The vectors are parallel.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of setting up a vector equation in this context?
To find the magnitude of the vectors.
To determine if the vectors are linearly independent or dependent.
To calculate the angle between the vectors.
To find the cross product of the vectors.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does a row of zeros in the augmented matrix indicate?
The vectors are orthogonal.
The vectors are linearly independent.
The vectors are equal.
The vectors are linearly dependent.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does it mean if the solution to the vector equation is not just the trivial solution?
The vectors are linearly independent.
The vectors are identical.
The vectors are linearly dependent.
The vectors are orthogonal.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of achieving reduced row echelon form?
It calculates the eigenvalues of the matrix.
It helps in finding the inverse of a matrix.
It simplifies the process of identifying linear dependence.
It determines the determinant of the matrix.
Tags
CCSS.8.EE.A.1
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What operation is performed to obtain a leading entry of one in the first row?
Adding a multiple of another row.
Subtracting a multiple of another row.
Multiplying the row by a constant.
Dividing the row by a constant.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does a non-zero solution in the reduced row echelon form indicate?
The vectors are orthogonal.
The vectors are parallel.
The vectors are linearly dependent.
The vectors are linearly independent.
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