11 Questions
Are the vectors 6, 12, 8, -2 linearly independent?
No
What does it mean if a column in the matrix is not a pivot column?
There is a free variable in the vector equation
If a set of vectors is linearly independent, how many solutions exist to the vector equation?
None
What do linearly dependent vectors imply about the constants in the vector equation?
They are all non-zero
How does a multiple of one vector affect linear independence?
Makes the vectors linearly dependent
What does it mean when a set of vectors is linearly independent?
The vectors have only the trivial solution to the vector equation
What is the characteristic of linearly dependent vectors?
They have multiple non-trivial solutions to the vector equation
How do you determine if vectors are linearly independent?
By row reducing an augmented matrix from the vector equation
When is a set of vectors considered linearly dependent?
When they add up to form the zero vector
What does it imply if a set of vectors is not linearly independent?
The vectors can be expressed in terms of each other
In what situation would a column in the matrix be considered a pivot column?
When it has a leading 1 after row reduction
Test your understanding of linear independence and linear dependence of vectors. Explore how to determine if a set of vectors is linearly independent or dependent, and the concept of trivial solution in vector equations.
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