Linear Algebra - Lecture 7 - Linear Combinations and Vector Equations

In this lecture, we discuss linear combinations and vector equations.

[@kamar1380]

1:36 2u+3v=(3,6,31)

[@shubhsheth]

Thanks, was wondering the same

[@Nanis-World]

I should have looked at the comments sooner lol I was like wait a second...2(0) is 0...and 3(1) is 3 soooo...how the heck did he get 2? Glad I wasn't the only one, phew!

[@beri4138]

Thank god I thought I was tripping

[@SteenGroentved]

Thanks!

[@Myfavoritecuties]

Thought so

[@JigarPatel28]

Love your math videos; it would be awesome if you can upload more of them with hard problems to prep for tests

[@ecru_5819]

Did in seven minutes what my prof spent an hour explaining
And I understood this faster - thank

[@touristofsongs4946]

:v

[@harshitpaliwal3430]

You had made a mistake in 2u + 3v

[@wjrasmussen666]

shouldn't the first problem result in [3 6 31] not [2 6 31]?

[@ronaldrussell2048]

Don't get me wrong, I truly appreciate the presenter's ability to greatly simplify the concept but the first answer is a profound arithmetic blunder that does not build confidence, leaving possibly subsequent problems in question.

[@daudmasih4739]

Yes it’s [3,6,31]

[@ninjapirate123]

yeah that was just a mistake

[@kimkakyeong]

1:19 the linear combination should be [3 6 31], no?
That aside, thank you for the video because you explain it way better than my uni lecture and textbook combined...

[@RobertManzano]

Thank you!
I was going crazy trying to figure out what I was doing wrong.

[@Myfavoritecuties]

@@RobertManzano same here

[@jacobm7026]

if you understand these fundamentals, everything just becomes harder algebraically. Understand these concepts and you wont have to worry about the prep

[@sofiastansbury7394]

Just to clarify,
b is a linear combination of v1 and v2 because there is a solution, and we know there is only one solution because there are no free variables in the reduced echelon form?

[@Brahma2012]

Excellent intro to Vector Equations

[@ninjapirate123]

This video is so helpful

[@chakoyotcheueliette1909]

thanks for the video . please can someone explain to me how the scalars are choosen pleasee

[@Odalo_3]

You teach soo well

[@The_Lucky_Chicken]

What does it mean by "no pivot"?

[@gulyatanbayeva]

thanks. your explanation was very good!

[@chicagomike6666]

great series...really appreciate you taking the time to do this...now maybe one on complex variables??

[@tinktwiceman]

Helpful like all the videos in your L.A. playlist. All hail King James!

[@anoshiravan6809]

thanks for your videos sir
it was so helpful

[@oliviadoulos4765]

very clear, thank you

[@kalharpatel4784]

Amazing

[@trigga9506]

U should break things down

[@maloumajok5192]

thanks you for your help 🙏

[@renk.574]

I just spent an entire hour trying to figure out why that was 2 instead of 3 D:
Shit happens though. Great video!

[@tomitomi7941]

Thank you, great explanation.

[@harshitpaliwal3430]

You teavh very amzingly keep it up

[@pez5491]

pivotal step of the solution is omitted in the vector equations part.

[@erickgaray463]

so beautifully put man thank you

[@delvin1751]

Man you are a legend

[@bernardmarukutu335]

very helpful . Upload more please.

[@mubangalillian2640]

hello, In the second example, how did you come up with the scalars -1,0 and 1/2??
even the first example why 2 and 3? i did note you made an error on the first example the resulting vector should be 3,6,31

[@HamblinMath]

I just picked arbitrary numbers. Any choice of three scalars would give a "linear combination" of those vectors. And, yes, there is an arithmetic error in that example (there are several other comments pointing that out).

[@erniesings6855]

excellent content

[@carlazacarias1810]

Thank you for these videos! Very helpful.

[@flyingscalpel7]

you the man!

[@ryanguo13]

thx

[@asif7240]

Thanks!

[@richardben-polo]

Hi, can you show how you got the equation to be reduced row echelon form?

[@HamblinMath]

This video explains the row-reduction process: czcams.com/video/72ysuwtYA0c/video.html

[@Rob-J-BJJ]

thank you jaes

[@Ssky38]

why is it vector (2, 6, 31)? Is that supposed to be vector (3, 6, 31). Thanks

[@victorgonzalezreyes16]

It's just a mistake. The correct answer is (3, 6, 31) :)

[@maryam-fu3mq]

much helpful

[@lemyul]

thanks

[@nischalsubedi9432]

could you clarify the pivot in the last column to determine if there are solutions or not? Does that mean non-zero entires?

[@HamblinMath]

I recommend watching Lecture 5 (czcams.com/video/kDbBTFvQgig/video.html) where I explain this concept.

[@nischalsubedi9432]

@@HamblinMathdo you have complete series on youtube? The playlist I used skipped lecture 4 and 5. Ok I will watch them. Great videos btw loved it!

[@cutcc]

This made things click, thank you ^_^

[@Wintersghost135]

👍

[@user-qv2gb5tj4w]

صياف محمد خلف

[@camerashysd7165]

there is a mistake in the first example

[@tonylin6893]

ok but why do you teach better than my prof?

[@harshitpaliwal3430]

You teavh very amzingly keep it up