Weekly Math Problem! #45

Diagonalization. I want to go over some linear algebra this week so, here is a problem to help me with that. I landed on diagonalization of a matrix because, for some reason, it stuck with me. I can't really explain why. Check out my other WMPs that involved working with matrices--WMP! #4 and WMP! #14. I don't have much else to say (due to tiiirrreeeddd-ness) 😩. 

⚠️Many steps involved.⚠️To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     How to perform row operations
        ✔️     How to find the determinant of a matrix
        ✔️     How to solve a quadratic equation
        ✔️     How to multiply matrices
        ✔️     How to find the inverse of a matrix

All calculations can be done without a calculator but, feel free to use a matrix calculator to check your work. Ready?? 😁🥴 WMP! #45 says...

Happy solving!

Check back on Friday, April 9th for the solution, which will be posted below ⬇️.

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Buy Me a ☕️ Coffee: TheYoungeLady ( I'm gonna need it this year. 😆 )

✏️📓 Solution Time! 📓✏️

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I'm just gonna go 'head and get into this calculation...computation...situation...

😅

Step 1. Find the Characteristic Polynomial

Step 2. Find the Eigenvalues 

Step 3. Find the Eigenspaces and Eigenvectors 

Step 4. Define Invertible Matrix, F, and Diagonal Matrix, D 

Step 5. Complete the Diagonalization

 

(Check the Diagonalization)

Step 6. Complete the Diagonalization

(Final Check)

**This plot was created using Desmos' Matrix Calculator.

WHEW!!! That was a lot. (You can't say I didn't warn you. With that...I think I'm gonna take it easy next week. 🥴)

▪️ Did you survive this calculation?

▪️ Have you ever taken Linear Algebra?

▪️ Leave your responses down below and let me know what you thought about this week's problem.

Thanks for solving with me this week!

Up next, WMP! #46.

Cheers!

The Younge Lady