Example of Diagonalizing a 2 x 2 Matrix

Linear Algebra: Let A = [3 1\ -2 0]. Find a 2 x 2 matrix P and a diagonal 2 x 2 matrix D such that P^{-1}AP = D.
Video Rating: 4 / 5

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1. You’re﻿ welcome!

2. You’re welcome! ﻿ I hope to be doing this for a while yet.

3. thank you, keep﻿ making videos…

4. tnx bob…﻿ i v completed a part of my syllabus at youtube… tnx a lot…

5. You need to find the null space of﻿ A-cI. If you haven’t mastered null spaces, finding eigenvectors will be tough.

6. You’re welcome! Let me know﻿ if you have any questions.

7. Doctor, thanks for your helpful videos, you’ve helped me a lot with my Linear Algebra lessons﻿ (my teacher makes us copy Howard Anton’s Linear Algebra book).

Greetings from Mexico

8. You’re welcome! Glad to be﻿ of help. – Bob

9. Thank you! This helped﻿ me so much!

10. Thanks for﻿ the high praise! I’m happy to take the assist, but those As have to be earned with your hard work. – Bob

11. You’re welcome! My odds﻿ got better – just got my brown belt in jiu-jitsu. – Bob

12. Speak softly and carry a big stick.
you’re a boss dood
-Tony﻿

13. Thank﻿ you helps alot.

If there was a battle royale of all math teachers I’d put money on you

14. You are EXCELLENT! best linear﻿ algebra teacher I’ve ever listened to! You have solely lead me to A’s in my math class

15. very nice, slightly above my level for now, but it should come﻿ within days. If I might make a suggestion: you’re a big man Dr. Bob, you block out half of your whiteboard at any given time. Could you put a shot with the entire equation at the end maybe? (just a few secs so we can pause the video and take a good look at the entire thing). Other than that: thanks!

16. These days it’s jiu-jitsu, but haven’t competed since 2010. Trained in boxing, muay thai, and vale tudo many﻿ years ago. It hurts longer when you get older. – Bob

17. do you box, or fight?﻿

18. You’re welcome! ﻿ – Bob

19. Thanks Dr. Bob!﻿

20. I totally botched that comment, so﻿ I removed it before it confuses anyone else. Sorry! I annotated the video since checking is a good point that can’t be repeated enough.

Thanks for the kind words! I hope I’m able to do this for a long time. – Bob

21. HI Dr. Bob..Thank you for answering my comment ..it seems i did not sort out the p inverse﻿ more carefully.. hahaha and you are right .the inverse of P is (1 1/ 2 1).. you are doing a great job sir ~! 🙂 keep up the good work

22. Hi Dr Bob …i would just like to check if my inverse of P @6:20 .is mistaken or correct .. shouldn’t it be the matrix I 1 -1 I and the lower part is I -2 , 1 I ??? i get first the inverse of P which is P^ -1 = 1/ (-1)(-1) – (2)(1) = -1 then multiplied it by -1 ..please correct me if I’am wrong ..you’ve done a great job﻿ explaining this topic very well and I am looking forward on more of your﻿ videos :).hope you could reply on this comment .Thank you again and God Bless ^.^

23. You’re welcome! -﻿ Bob