@Ph0Xy the goal is to get (A-I)*[v1;v2;v3] = [0;0;0]. Since the first column of A is all zeros we can conclude that the first number (v1) is the 'free variable'. This is because none of the equations we can set up ( ie 0=2(v2)+3(v3) , 0=-2(v3) , and 0=1(v2)+3(v3) ) will contain v1 in them. This allows v1 to take on any value and still have it satisfy the system of equations. The other two variables can be easily shown to be 0. This gives us the eigenvector [C;0;0] where C=constant. He pics C=1

Sure thing. We are left with the following set of equations: 0 = 2*v2 + 3*v3 0 = -2*v3 0 = v2+3*v3 The second equation gives: v3 = 0 when plugged into the third equation, you get: v2 = 0 Which gives you the answer, plugging both back into the first equation confirms our answer: 0 = 0 Hope that helps :D

Thank you MIT for making such videos. It has been so helpful for me!! Thank you so much! Please continue to make more of such videos.

very explanatory, thank you!!!

This problem also shows a property of singular matrices that I didn't think of before: notice that in this case the inverse of A minus the identity produces a singular matrix; also from the formula given to find the eigenvalues of this matrix (1/lambda) - 1, for lambda = 1, we get 0. It shows a matrix is singular if one of its eigenvalue is 0, which is the same as saying its null space is not empty. Not mind blowing I know, but maybe a useful piece of trivia for the next dinner party.

@618361 can you explain why the other 2 variables is zero? i always stuck at this part.tq.

This guy seemed to be happy to finish this question Lolz

I remember all this material from Prof. Gilbert Strang's 18.700 class ("Linear Algebra") back in 1973. I'm from the Class of '75. I loved the vocabulary of linear algebra -- eigenvectors, eigenvalues, Gauss-Jordan elimination, Hermitian matrices, determinants, etc. The problem sets were awesome! I used to do them while I was watching my daily repertoire of afternoon soaps at MacGregor House. I'm currently working with KZreadrs JustVisitingNYC and CaspaNarkz102. Check us all out.

THANKS, it was helpful

How did he get the formula at

1:10 "hi again" or "EIGEN"?

its too short cut.. appreciate if you can do everything step by step and complicated 3x3 matrices rather than 1,0,0.. cheers

circles

I'm going in circles