Linear Algebra 4.2.1 Null Spaces

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Kimberly Brehm

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It is currently 3 am as I study for my linear algebra midterm usually I'd be falling asleep at my desk but you do such a great job of explaining and engaging I somehow manage to plow through your videos so easily thank you so much

zbelzheng

These are the best linear algebra videos I've found so far. Great Job!

queenstrategy

For those that don't get 13:00.
After getting RREF, we decompose the vector giving the general solution into linear combination of vectors where the weights are the free variables. That is,
x1 |2 * x2 + x4 - 3*x5 |
x2 | x2 |
x3 = | - 2*x4 + 2*x5 | = to the final solution she had at 14:35
x4 | x4 |
x5 | x5 |

Sora_Nai

THANK CHRIST FOR TEACHERS LIKE YOU ON YOUTUBE!!!! WOW! ENJOYING MATHS FOR THE FIRST TIME!

lempuujjj

13:06 This makes sense up to here. You just rearranged the augmented matrix for x -2.x2 -1x4 +3x5 = 0 (ect) but where does the x2 [2 1 0 0 0] come from? That seemed to appear out of nowhere.

The pattern seems to be:
(1) find the pivots for each row. If a column (x1...xn) doesn't have a pivot it is free
(2) for each pivot, rearrange the algebraic equation to isolate the dependent variable x1, x3 ect (PS: not sure why you couldn't continue with row operations to remove x4 from x1 or x3 equations)
(3) for each free variable set it to 1, the other free variables to 0
This will give you the coefficients for the dependent variables. Arrange them in the appropriate row

Is this a new algorithmic approach is new or have I missed a video?

mightyhorst

Don't you mean always linearly dependent on 16:12? because you are essentially stating that they are free variables so the scalars don't have to equal to zero, so the trivial solution has more than one possible scalar numbers

amazzaleen

Without these types of YouTube videos, I would have no shot of making A's in any of my classes. Unlike my other classes that I understand most stuff in class but just need refreshers from videos to help me study.. For this class on the other hand, I do not understand anything in the class 😂😂😂 I really need these videos. You're gonna carry me to my D. A C would be the Lord's blessing 😂I do not want to graduate late or have to retake this class!!!

pandaonsteroids

this is so so so awesome oh my god thank you so much

xcl

late to the party, but thank you for uploading these. Helping me big time late in the semester!

nathanfitzgerald

I do not understand why the set is linearly independent if there are free variables in the spanning set. Please explain!

jacobgavilanez

i didn't understand at 14:22 of how you come up with x2(2, 1, 0, 0) ...
If someone knows plz tell me

rashidyaseen

Hi, I don't understand why you put 1 for free variables inside the nx1 matrices.

jeff_kola

At around 5:00 what you're writing for conditions 2 and 3 isn't correct. Condition 2 should say: "When u and v are in Nul(A), is u+v in Nul(A)?" Condition 3 should be: "When u is in Nul(A), is cu is in Nul(A)?"

cooking

Why does x belong to Rn for null space? I always see that in notes but I am unsure of why and I cant seem to visualize it.

susandavis

If this is not the best then I don't know what is...

mokoepa

why must the pivots have 0s above and below?

monoinluv

I hope you don't mind but I'm playing the video in 1.25 :)

rfb

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