Eigenvalues. This week, linear algebra came to mind. The last time I did a linear algebra related problem on this blog was in WMP #45. Check it out...it may help you with this week's problem. π *clears throat*. Anyhow, eigenvalues are cool and have lots of applications. For more info, check out the Applications of Eigenvalues and Eigenvectors page from Interactive Mathematics website.
To solve this week's problem in completion, you need to recall the following math skills:
✔️ How to find the determinant of a 2x2 matrix
✔️ How to solve a quadratic equation
WMP! #70 wants us to...
Check back on Saturday, January 22nd for the solution, which will be posted below ⬇️.
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✏️π Solution Time! π✏️
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πΆLet's get it started...πΆ
The process to finding the eigenvalues of a 2x2 matrix requires working with a polynomial called the characteristic polynomial. Ours will be a quadratic polynomial generated from finding the determinant of (Y - Ξ»I2), where I2 is the 2x2 identity matrix.
Now that we have the characteristic polynomial, we need to find it roots. The roots of the characteristic polynomial are the eigenvalues of the matrix. Set the characteristic polynomial equal to zero and solve. Ours is factorable, but if it wasn't, then you'd have the option to use other methods for solving a quadratic equation.The eigenvalues have been found!
▪️ Hopefully you haven't found the process to finding the eigenvalues of a 2x2 matrix daunting.
▪️ Let me know what you thought about this week's problem in the comments section.
Thank you for solving with me this week. π
π WMP! #71 is up next.
Cheers!
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