Example of Basis for a Null Space

Linear Algebra: Find a basis for the null space of the matrix A = [ 1 0 3 2 1 \ 0 2 2 4 4 \ 0 0 0 2 6 ]. We use reduced row echelon form to assign dependent and independent variables.

[JoshMacDonaldsChannel]

The reason your videos are better than the rest is because they are short, organized and to the point. Students don't have time for a 15 minute video.

[tyreloulton]

Clear and concise, you may have just saved another helpless linear algebra soul. Well done! Keep them coming!

[MrEditorBen]

You explained in four minutes what a textbook and my professor couldn't. Thank you

[icecoldpierre]

The first thing I noticed about this video is you did the problem ahead of time so you can focus only on explaining it in the video. Well done!

[Ydmaster]

I usually don't comment on videos but I have to say, you are a man of knowledge. Thank you. I learned a lot thanks to you.

[missflecha]

you have made a very stressed engineering major very calm on the eve of her linear algebra final. you're the best!

[sault]

Just found this channel but I'm already a big fan of Dr. Bob and his cool pointing rod

[devinmurphy]

MathDoctorBob is comin in clutch again with the linear algebra guides. I think one of the biggest struggles and faults of a large majority of linear algebra explanations and proofs is that they are EXTREMELY detailed, and difficult to follow (think all those proofs you'll see with slews of variables, notations, etc). They're super hard to follow. I love how you're straight to the point, and give a couple different "names" for each of the things you reference (pivots vs dependent variables, etc). Makes this not only easier to follow, but much easier to understand. Cheers from Uni of Illinois at Chicago!

[ambrose_]

You make the best math videos ive seen so far. No bs. Straight to the point. Thank you.

[TheJediBendu]

Spent so many hours reading my textbook and not understanding it. Your short video is so clear, thanks a ton

[TBV]

You are legendary...this is the best online tutoring I ever had. All I had to do was pause and take notes!!! Rather than others where I had to rewind several times to get it. Keep it up Dr Bob!!!

[tobypham]

This guy is doing rows in the gym and in the classroom... and he has perfect form in both👀

[ImmortalScrub]

You, sir, are my hero. After spending an hour and a half digging through google searches and finding multiple different explanations that didn't make any sense, you taught this to me in 4 and a half minutes. Well played

[nnovnn]

You speak so clear and never use words like uuhhmm or uuuh. Perfect!

[trevydandridge]

Woah!!! You're the buffest Linear algebra nerd I've ever seen-- I will be like you.

[squkyshoes]

This is the most fullproof method of finding the null space I've found (because my prefessor doesn't explain how to solve things, I have to look them up). All the other methods I've looked at were wishy-washy, but yours is spot on! Thanks for posting this!

[MrMinefinity]

This just saved me from a mental breakdown

Edit: turns out it gets a lot harder

[MathDoctorBob]

@Hockeysktr17 The main point here is reduced row echelon form. It enables two things: 1) we compute vectors directly from the independent variables - no back substitution needed, and 2) the 0-1 recipe guarantees linear independence.

If you form a matrix B from these vectors, the independent variables correspond to rows of zeros with a single 1. These 1s correspond to pivots, and there will be a pivot in each column, which is the test for LI. (Out of space - more to say if needed) - Bob

[MathDoctorBob]

Thanks! Glad to be of help. Null spaces are extremely important for what comes next: eigenvalues and eigenvectors. I have you covered there also - check the playlist, although the website is easier to navigate.

[Mr_Waffle.]

I didn't understand my lecturer's notes at all on this, but after watching the video I was able to get full marks for the question in my assignment. You're the best Dr Bob!