
Understanding Linear Independence of Vector-Valued Functions

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Mathematics
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11th Grade - University
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Hard
+1
Standards-aligned

Aiden Montgomery
FREE Resource
Standards-aligned
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the condition for vector-valued functions to be linearly independent?
The only solution to the vector equation is when all coefficients are zero.
The functions are orthogonal to each other.
The coefficients of the functions are all non-zero.
The sum of the functions equals a non-zero vector.
Tags
CCSS.8.EE.C.8C
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the first method, what is the initial step to determine linear independence?
Check if the functions are orthogonal.
Find the inverse of the matrix.
Write the vector equation.
Calculate the Wronskian determinant.
Tags
CCSS.8.EE.C.8B
CCSS.HSA.REI.C.6
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens when you add the two equations in the system of equations?
The equations become dependent.
The equations become identical.
The second terms cancel out.
The first terms cancel out.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why must C2 be zero in the system of equations?
Because e to the three T is never zero.
Because C1 is zero.
Because e to the three T is zero.
Because the equations are dependent.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the Wronskian used for in the second method?
To find the inverse of a matrix.
To determine if the vector-valued functions are linearly independent.
To solve the system of equations.
To calculate the eigenvalues.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does a non-zero Wronskian determinant indicate?
The functions are linearly dependent.
The functions are linearly independent.
The functions are identical.
The functions are orthogonal.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the determinant of the matrix in the second method?
8 e to the two t
14 e to the two t
6 e to the two t
12 e to the two t
Tags
CCSS.HSA.REI.C.9
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