EXAMPLE: Finding a basis for a subspace defined by a linear equation

[@anushachaudhury9455]

THANK YOU SO MUCH YOU HAVE NO IDEA HOW MUCH THIS SAVED ME...I WANTED A SIMPLE EXPLANATION WITH A SIMPLE EXAMPLE FOR SO LONG

[@twa_le]

wow this video attracted a lot of attention, it comes to show that it is important to understand the basics before jumping into harder and more complex problems.

[@SAXYmonster]

Don't know why people dislike this... Thanks a lot!

[@uran_khatolaa]

This helped me so much!! This was exactly where I was struggling in all questions

[@daddyvader9595]

Well done. You made this very clear and concise. Thank you!

[@yeswecan7244]

Thanks a lot Sir.... Actlly strgllg to solve such questions but ur this video just made it vry easy😊

[@YunisRajab]

This was a life saver. Thank you so much.

[@chestccj7955]

dude you rock! Thanks for sharing, really helped me when doing linear algebra assignment

[@MrAvancini]

Thank you! My prof. complicated this soooo much !

[@norhidayahnordin4045]

Hi, i just want to say thank you so muchhh bcs this is similar to my test question and I've been searching for a hint and i found it! Thank you!

[@siren575]

What would we do if we were given two conditions (so 2 equations equal to 0 instead of one equation)?

[@mathslearningUofA]

I would rewrite the two equations as a matrix, and do this: kzbin.info/www/bejne/lYfaiIetm92Jr80

[@ricardomarino8554]

Not all the heroes wear a cape, someones do great videos like this

[@mathslearningUofA]

Aww thanks.

[@pulp6667]

Great video, thank you very much.

[@sravanisravs778]

Nice explanation.......cleared my doubt

[@deepaksharmavishnu]

Thanks a lot Love from india

[@ishi8112]

Thanks, this helped. The dimension of the subspace is 3, so would it be in R^3?

[@mathslearningUofA]

+ishi8112 No, the subspace isn't in R^3, it's in R^4. Being in R^n is about how many coordinates your vectors have. These vectors are in R^4 since they have four coordinates.

[@mathslearningUofA]

The subspace is a three-dimensional object sitting inside R^4. So it's the "same shape" as R^3, but it's made of vectors with 4 coordinates.

[@ishi8112]

Ooooh, thank you for your reply, I understand now (just in time too, exam tomorrow) ^^

[@ernestodiaz8620]

How can we have a z component when we dont have a z variable in the equation?

[@mathslearningUofA]

This set is made of points with four coordinates, and the equation is a way to tell if a point is part of this set. The equation doesn't happen to include z, which is ok. It means that the z-coordinate is not part of the decision of whether a point is in this set. But the z-coordinate is still part of the point itself.

[@angelchinda2604]

Literally a godsend

[@Warriorpend2]

I greatly appreciate this. I was very confused. Now it all makes sense. ^^

[@msamsa5819]

That's a powerful example

[@blashernandez3624]

Thank you sir. You have helped me tremendously.

[@pandacutiesuperstar]

But what if there is two within one like B = {(x,y,z)| x+y+z =0 and x-y-z =0}

[@1USF]

i solved it but had different set of vektors: x(3;000) + y(0;1;0;0) + z(0;0;0;0) + t (0;0;0;-7) wich is also Dimension 3. is this a correct way?

[@mathslearningUofA]

+Joe Liban No this is not correct. The equation is a condition that the x, y, z, t coordinates must satisfy in order for a point (x,y,z,t) to be in the subspace. The numbers in it do not directly describe what the coordinates of the points look like. Note that if the equation had been 3x +y =0, then the points would be of the form x(1;-3;0;0)+z(0;0;1;0)+t(0;0;0;1), which is still three-dimensional.

[@janetpinto1325]

very good explanation

[@presentlymine]

thanks for this video! simply explained! :)

[@lesegomokgabudi5798]

Thanks a lot

[@vivekg6209]

Really helpful, thanks

[@ahmafa956]

Much love to ya!

[@jzo08]

Thank you!

[@FahimAhmed38]

you are a lifesaver :D

[@EsKaioS]

Didnt know we had a youtube channel lol.

[@triptidahiya1619]

Thanku very much sir

[@vulamnguyen6750]

thank you so muchh

[@merhiyoussif]

THANK YOU!

[@Sanji.A.Hewson]

THANKS!

[@simasimo9796]

2018 who else?

[@Mike7064]

Didn't understood anything :(