Check for Linear Dependence (3 functions, using definition)

TL;DR

Learn how to determine linear dependence of Street functions through finding constants in a system of equations.

Transcript

in this video I'm gonna show you guys how to show Street functions are linearly dependent on interval in a previous video I show you guys how to show two functions are linearly dependent or not to do that for two functions all you have to do is check if one function is a constant multiple of the other or not right but for stream functions like this... Read More

Key Insights

• 🚱 Linear dependence of Street functions involves finding non-zero constants c1, c2, and c3 in a system of equations.
• 👍 Matching coefficients and solving equations are essential steps in proving the linear dependence of Street functions.
• 🛀 Selecting suitable values for the constants shows the relationship between the Street functions.

Questions & Answers

Q: How do you determine if Street functions are linearly dependent?

To show linear dependence of Street functions, you need to find constants c1, c2, and c3 such that they are not all zero and satisfy the equation c1y1 + c2y2 + c3y3 = 0.

Q: Why can't you simply check if one Street function is a constant multiple of the other to show linear dependence?

Unlike simple functions, Street functions require finding non-zero constants in a system of equations to demonstrate linear dependence, as one function may not be a direct multiple of the other.

Q: What is the significance of finding constants c1, c2, and c3 in proving linear dependence?

By solving the system of equations with the given Street functions, the values obtained for c1, c2, and c3 show how the functions are related and whether they are linearly dependent.

Q: How does matching coefficients and solving equations help in showing linear dependence?

Matching coefficients and solving equations allows you to find suitable values for c1, c2, and c3, proving the linear dependence of the Street functions by demonstrating a solution other than all constants being zero.

Summary & Key Takeaways

• Showing linear dependence of Street functions involves finding constants c1, c2, and c3 in a system of equations.

• The condition is that the constants cannot all be zero to show linear dependence.

• By solving the system of equations and finding suitable values for the constants, you can prove linear dependence of Street functions.