CSIR NET DECEMBER 2018 LINEAR ALGEBRA COMPLETE SOLUTION

[@jhulanacharya4513]

Thank u sir...for such a helpful video. I just pointed out that in the last question @1:49:00 time..there is a small mistake about to finding the eigen values. Plss check it sir...and hope you will upload more this type of helpful video.. Thank you sir.

[@piyalikarmakar5099]

at 35:00 you can simply take Tr(MPM*)=Tr(M*MP)=Tr(IP)=Tr(P)

[@Dearbhanusir]

M ese hi video ki talash m tha Jo questions hi na karae sath ki sath concept bhi clear kre..kyoki maine coaching nhi ki ..thank you so much sir

[@mathematicalPathshala]

Good luck for your exams😃😃

[@rohitsharma-fw2fy]

Sir, in question 4, eigenvector x of (A+i I)^-1 is not same as eigenvector x of (A-i I). So, I think last step (A-i I)x/(lambda+i)=(A+iI)^-1x implies that (lambda-i)x/(lambda +i)=(A+iI)^-1x, is not correct. Please clearify me if i am wrong

[@renuc.r8848]

sir in 31 :13 M is n×k matrix. so not a square matrix. then how is M and M*invertible ? plss reply..

[@mathematicalPathshala]

Thanx for observing this I mistaken there but u can think in this way M is n*k made by orthonormal vevtors so M will keep full rank(full rank means Rank(M)=min{n,k} ) so after taking MPM* since M and M* has full rank so it won't affect the rank of P so rank will be k Or U can just find the matrix MPM* explicitly then u will get

[@renuc.r8848]

Thank you sir for your valuable time.

[@souvagyamaity2000]

Exactly same question came to my mind and for answer I started scrolling in comment box . Here this is. Thank you both .

[@souvagyamaity2000]

Sir, I think this comment should be pinned.

[@abhishekmodi7761]

Sir , csir net k part C me real analysis me mujh se maximum 3 se 4 questions hi ho pate h , out of 9 questions from pyq . Meri condition ok h ya km h . Maximum average students part C real analysis k kitne problems attempt kr lete h ,please tell me . I will take first attempt this June 2023 session

[@arunnagargoje1439]

Very nice explanation sir. It's helpful thank you so much👌👌

[@bikashdutta2585]

Very good explanation of sir🙏🙏🙏

[@piyalikarmakar5099]

while solving a question, please add the detailed explanation on why an option is wrong.

[@sayansaha6393]

Sir,at 6, can we show positive definite by Eigen value??

[@Dearbhanusir]

Thank you so much sir😊

[@mathematicalPathshala]

Most welcome

[@netpracticecsirnetmathemat4964]

In question no. 12 how can you be sure that M(uu*)=( uu*)M, in the multiplication {M-lamda(uu*)}{M-lamda(uu*)}^(n-1)? As per my knowledge if A, B are hermition matrix then (AB) need not be hermitian in general. Please correct me if I'm wrong

[@mathematicalPathshala]

You are correct but where you have doubt in my argument?

[@zakiralam3489]

Lamda(uu^*) (M^n-1 ) = lamda(M^n-1) (uu^*) how u write this term equal since in general matrix multiplication not commute.........

[@aanchal4310]

Wow 😊😊

[@mathematicalPathshala]

Thanks for the appreciation

[@echan9320]

Than you so much sir

[@gracefully9699]

Thanku sir...it was very useful...can u plz upload a video on inner product space and bilinear form on the basis of previous year csir questions

[@mathematicalPathshala]

We have uploaded all the solutions of csir net linear algebra u can watch them and if u wanna study whole linear algebra u can get them at mathematicalpathshala.com but those are paid

[@sayansaha6393]

Mod rank A- rank B

[@sayansaha6393]

Any recommendations?

[@soumyajitkundu3663]

sir when will linear algebra next lecture vedio be uploaded? is linear algebra complete for net,gate?

[@mathematicalPathshala]

No inner product,bilinear form,norm,orthogonality are remaining

[@malkeetsinghbharaj2802]

9th sum ki last option mein mujhe problem lag rhi hai . Apne vo solv kaise kiya sir .ek baar dekhna isse

[@mathematicalPathshala]

Yes little calculation mistake thanx for noticing (please make it correct at 1:09:11(in finding roots)

[@malkeetsinghbharaj2802]

@@mathematicalPathshala Sir after solving roots comes out to be 1 & -4, still i have doubt . Option true hoga jaa nhi . Agar true hai hai to kaise .plz explain sir 🙏🏻 aacording to me option 4 is fasle

[@mathematicalPathshala]

Send me your solution at 8218203410(WhatsApp)

[@sonasinghchawda1472]

Sir 4th option true hai ya nhi

[@sanjaypaul4869]

does minimal polynoial contains all eigen values?

[@sushmajangra234]

Yes . But sometimes without algebraic multiplicity

[@niket-3]

Thank You Sir

[@mahendarreddy2260]

Option (d) for n=n how sir

[@navdeepvarshney6422]

Bhai Q12 m matrix product commute nhi krta ek Baar dobara krke dekho

[@ambatimeghana6980]

After completing solution please write option answer

[@shaktidivas3349]

Sir diagonalization lecture phir ek bar upload karo

[@mathematicalPathshala]

You may get on play.google.com/store/apps/details?id=co.lynde.unflv

[@mahendarreddy2260]

Question no 12 we can't andastading sir

[@tanushreebiswas9394]

Thanks Sir

[@mathematicalPathshala]

Keep learning

[@shishupalsingh9579]

sir please uplode jordan canonical form

[@PankajGupta-sy7uf]

I think 3-d is correct because w1+w2=R4

[@PankajGupta-sy7uf]

*d nhi b

[@ameethhamse157]

Nice video

[@eshwarp138]

👌👌👌👌