Proving a Set of Vectors is a Basis - Linear Algebra

[@random_sinner]

Any combination of 3 linearly independent vectors should span R3. We could just take the determinant of 3x3 the matrix [t1 t2 t3] and since it's non zero, the 3 vectors are linearly independent.

[@DrewWerbowski]

Yes, you're right! In some intro level courses at my university, some professors don't like to give full marks for stating 3 linearly independent vectors in R3 will span R3 if the concepts are new; they want you to show why that would be true with a more rigorous approach like in this video.

[@dehey4310]

This was the video that I was looking for... Thanks love from srilanka

[@アナキンスカイオ一カ]

I truly appreciated the video of yours. Nevertheless, an algebraic mistake has been made in the minute 07:45, when thou was subtracting the third row by the first one. It has been forgotten to make the multiplication by the signals, henceforth, that part becomes quite uncertain. Nonetheless, thy proof is magnificent!

[@DrewWerbowski]

Good catch, it should read c3 = x3 - (x1)/2 + (x2)/2

[@alexandonov8253]

Thank you so much, your video was so helpful

[@angelosdelta8888]

Hello Drew, thans for the awesome work. I have a question. If we prove that those vectors span the whole R3, then isn't it obvious that they also have to be independent, considering the fact that if at least one mas not linearly depended on the others, then the space produced from the linear combinations would be just a plane of the whole space? I have seen again this kind of proof and I am a little bit confused. Thank you in advance!

[@DrewWerbowski]

Great question. Fair warning: my background is engineering, not math, so people studying pure math can feel free to chip in here. How would you prove those vectors span R3? I see your logic, but I’m not sure it’s rigorous enough to just claim “since the vectors span the entire vector space, they must also be linearly independent” for our proof. I seem to remember this explanation not being sufficient during tn studies. I would suggest looking into the theorem where this logic comes from to explore this further

[@alifruslan2728]

Nice way of describing, thanks.

[@RohanKumar-l5d]

Got it sir.

[@RanbirSingh-no3mc]

Nice work man! Can you make a video on Waterloo Works?