JEE Mains 2024: Solve Matrix Polynomial with Cayley-Hamilton Theorem | Characteristic Equation | PYQ

JEE Mains 2024: Solve Matrix Polynomial with Cayley-Hamilton Theorem | Characteristic Equation | PYQ
In this video, I discussed a JEE Mains 2024 matrix question involving a matrix polynomial equation. The solution revolves around the Cayley-Hamilton theorem, which is one of the most important concepts in matrices.
By understanding and applying this theorem, you can solve complex-looking matrix problems easily. This concept is crucial for JEE Mains and Advanced aspirants as it not only saves time but also ensures accuracy.
I’ve explained the Cayley-Hamilton theorem in a simple and effective way, making it easy to grasp and apply. Watch till the end for tips and tricks, and don’t forget to attempt the homework question shared at the end!
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[@alokdamodar]

Thank you sir❤❤

[@factorialacademy]

most welcome

[@somuapti]

Excellent explanation.

[@JadenIIT]

thanks for quick revision

[@factorialacademy]

most welcome

[@nishitdhimant47]

How do we know if the given equation is necessarily the characteristic equation?

[@rishabhtiwari2325]

Uniqueness of chr equation of matrix

[@nishitdhimant47]

@rishabhtiwari2325 Thanks. Got it.

[@gauravwadhwa2817]

@@rishabhtiwari2325pls explain a little more , you mean if there’s a equation for a matrix given like this , it would be the characteristic equation only?

[@rishabhtiwari2325]

@@gauravwadhwa2817 yes if there is a polynomial equation in some matrix A then that has to be the characteristic equation as A does not satisfy any other polynomial

[@gauravwadhwa2817]

@@rishabhtiwari2325thanks 🙏

[@Ajit-45s]

Concept cleared ❤❤

[@CivicBitcoin]

Bhai tu har jaha dikhta ha mujhe 😂😂

[@dhhonii_]

THANK YOU SIR !!

[@Ishowmik3y]

Sir questions on adjoint matrix

[@jee1000-f3i]

sir plz make complete sol. of 2024 pys chap wise , if concept is repeated then u can give it for hw, i like your explanation and it is really helpful

[@JEENimai]

Dhanyavaad sir

[@editor7999]

Sir Agar Ho Sake To Is kuch Din Bich Me Ap Top 5 PYQS FROM EACH CHAPTER LEKAR AO.. PLZZ✨ Jisme Concept Cover ho jaye

[@Jee-l1n]

Hi sir i was on a dopamine detox and serious prep for 45 days my jee mains is on 22 jan, I've completed and understood everything by heart in maths but I've only completed these chapters: quad, sns, binomial, trigo, st lines, circles, ellipse, hyperbola, parabola, statistics, limits, functions, itf, continuity, differentiability, mod. Is it enough for 10-16 questions?? Or should i do vector and 3d?

[@AbhirudhTelugu]

Which shift on 22 nd jan?

[@Jee-l1n]

@AbhirudhTelugu shift 1

[@AbhirudhTelugu]

@@Jee-l1n nice

[@AbhirudhTelugu]

Don't worry

[@factorialacademy]

Yes this will cover 10-15 questions
But I would suggest you to do vectors and 3D

[@SHRIXJOD_GAMING]

-21 ke equal rehne wala hai how? 5:27

[@lohithkiran3739]

It's similar to product of roots in cubic i.e is -d/a
Here it is -21/1=-21

[@abhyam_6996]

Q m jo equation diya hai, vo check karna parega na ki vo uska characteristic equation hai ki ni?
Pata kaise chalega ki jo equation diya hai question m, vo uska characteristic equation hi hai

[@opguy_219]

Hm 🤔

[@rishabhtiwari2325]

Characteristics equation for every matrix is unique

[@fullmasti7365]

Trust the examiner 😊

[@adzcreativity8660]

bhai A satisfies the equation as given in the question
so we can say that it is the ce of A because matrix has only a unique ce.

[@Madira.Vijaya]

Sir Bayes theorem mai dho question karo

[@factorialacademy]

done

[@Madira.Vijaya]

Thank you very much sir 🙌🙌