Rank and Solving Ax=0

[@mees271]

Thank you very much! This really helped me out. You are a great teacher :)

[@Crosswalknorway]

A really clear and helpful video! Just wanted to say thanks!

[@danielavrit4526]

Thanks for the video! This really helped me. I have an exam coming up, and my teacher wants us to express solutions in parametric AND parametric vector form.

[@informationisallabout8976]

Find the number of parameters in the solution set of Ax=0 if A is a 5x7 matrix has 3 pivot columns

[@akahn8311]

Saved me hours of reading, Thanx a ton !!!

[@neettim]

I have 2 questions: 1. Can you please explain to me what Ax = 0 means? Also what does the 'x' mean? I know A is the matrix but what is the 'x'? 2. In the 2nd example how did you get that linear combination at 7:20? You didn't explain how you got the entries for: x3 ( entries ) + x5 (entries). Please help

[@lorenzosadun565]

Ax is the product of the matrix A with the vector x. For this, and for your second question, take a look at my previous videos, "Matrix multiplication" and "Row reduction, row-echelon form and reduced row-echelon form".

[@neettim]

Lorenzo Sadun alright, thank you!

[@matthewjames7513]

Thank you for your video! This was a good refresher! I have a question though! I know that the solution to Ax = b is x = 1/det(A) adj(A) b. So this shows us that x can only have solutions if det(A) # 0. Why then, when we're solving for non trivial solutions (x # 0) to Ax = 0 do we solve for det(A) = 0 ?? In my Engineering class they say det(A) = 0 but then that would mean x = 1/0 adj(A) * 0 = math error :/ I'm really confused! Please help :) Thanks!

[@ismaileyaqub6335]

can you use just row echelon form to solve the equations?

[@lorenzosadun565]

+Ismaile Yaqub You can certainly use row-echelon form (REF) to solve the equations, but with reduced row-echelon form (RREF) you can pretty much read off all of the solutions. With REF you still need to do a bunch of back-substitution. On the flip side, if all you care about is how many solutions there are (or more precisely, the dimension of the space of solutions), then you don't even need REF. You just need the rank.

[@ismaileyaqub6335]

got it, cheers! your videos have helped me tremendously in first year physics. thank you :)

[@ProudRich]

Thank you . Really well explained .

[@charlesn9788]

this helped a lot! thanks

[@mikecole5485]

wow, and what if all your pivots aren't 1's and 0's...