Check for Linear Dependence (of 2 functions) | Summary and Q&A

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March 16, 2017
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blackpenredpen
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Check for Linear Dependence (of 2 functions)

TL;DR

Learn how to determine if two functions are linearly dependent by checking if one function is a constant multiple of the other.

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Questions & Answers

Q: What is the key method for determining if two functions are linearly dependent?

The key method is to check if one function is a constant multiple of the other. If a constant multiple can be found, the functions are linearly dependent; otherwise, they are linearly independent.

Q: What is the significance of checking for linear dependence or independence of functions?

Checking for linear dependence or independence helps determine if two functions share a relationship and can be used to simplify equations or solve systems of equations.

Q: Can "e to the 3t" and "e to the 60" be considered linearly dependent?

No, these two functions cannot be considered linearly dependent because they are not constant multiples of each other. There is no constant value that can make them equal.

Q: How can you determine the linear dependence of the functions "T squared minus 9" and "T plus 3"?

In this case, the two functions are linearly independent because they are not constant multiples of each other. Although they share a common factor of "T plus 3", there is no constant that can make them equal.

Summary & Key Takeaways

  • The video demonstrates how to check if two functions are linearly dependent or independent.

  • For two functions, check if one function is a constant multiple of the other.

  • If a constant multiple can be found, the functions are linearly dependent; otherwise, they are linearly independent.

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