Was worried when I saw this was 56:57 mins long, but honestly this is the best explanation I've come across. Better than my lecturer and Khan Academy. Keep up the vids!
Well explained but you made a minor error when finding the elements in the kernel. The last vector should be t [0 0 -2 0 1],but you have t [ 0 0 -2 0 2] . Since x5 = t and not 2t.
haha was watchin this video before exam just for a recall xd its makes me laugh the way u describe everything. in a good way of course :) . comparing to my teacher u make it just so easy and smooth . we the people need this . big thanks man ,
This video is perfect for dumb people like me. Haha, just kidding, but it's such an amazing video. Explanation - on point. Pace - On point. Examples - On point. Everything - On point.
Thank you for the Extremely clear and slow paced explanation. My professor waffled about for on these 4 concepts for 2 weeks and I never could make heads or tails of her work. I hope your students acknowledge how lucky they are to have you.
I am so grateful your explanation in details. it is so much helpful for preparing my final. i was confused many things when i learned it in classl. Thank you so much again.
I know this is an old vid, but you are such a life saver. I learned more from this vid than I learned from my professor, and it's really sad tbh. Thanks for this!
ehhhhhh im stuck with Orthonormal Basis of image for a 4x4 matrix.... is it just following the steps to get the image and divide each of them by norm to get the orthonormal one?
The vectors in an orthonormal basis also have to be pairwise orthogonal. After you find a basis of the image of your matrix, you will need to apply the Gram-Schmidt Algorithm to transform your basis into an orthogonal one. Check out: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-dCN7zzBBEwY.html All that's left after is to normalize the vectors by dividing them by their respective norms.
So the section around 22:00, the method he uses to find the basis of the plane is - I thought - the method for finding the basis of the null space. Is that not correct?
I followed everything that was done, but why is it done? The free variables confuse the hell out if me. I was under the impression that solving for n variables with less than n equations wasn't possible?
+Putins Cat Any homogeneous linear system with more variables than equations has infinitely many solutions. Consider the simple example x-y=0. The solutions to this equation are all the points on the line y=x.
slcmath@pc Sure, but what is with the r,s,t variables? I can replicate what was done, but why? When you multiple matrices, you take each row against a column vector, but then you can also take a matrix and split the columns into vectors and say cV1 + cV2 + cV3. I have no idea what that is about.. Is it just something that is what it is?
I thought if there is any solution except 0,0,0 it is linearly dependent. here there is solution -6,1,0 why it is not linearly dependent? Also about dimension, I thought detention is 3 because there is 3 variables which are x,y,z
If the only solution is the zero solution, then the vectors are linearly independent. If there exists a nonzero solution, then the vectors are linearly dependent.
Yes.. there is nonzero solution which is -6,1,0 then it should be linearly dependent according to definition as you said, but you said that is linearly independent.
