PreCalculus - Matrices & Matrix Applications (9 of 33) Gaussian Elimination: 3x3, Infinite Solutions

In this video I will use the method of Gaussian elimination to solve for a system of 3 linear equations with infinite number of solutions.

Next video in the Matrices series can be seen at:

[busolaakintope]

loved this, i wish you were my lecturer

[andyp]

Thank you for making this. A good video, though I think It would be more clearer as to what's trying to be achieved here if you went through to show the infinite solution set. ie non-trivial solution. just my 2 cents : )

[tahirimathscienceonlinetea]

You're fantastic explained that 👍👍👍

[rob]

Here we have an infinite solution. That is right but it doesn't mean we can plug any value of x, y, and z to solve all three linear equations. Example (1, 2, 1) cannot be a solution for the given system of linear equations. So, our solution set would be {7a-5, 1+3a, a} when 'a' is any real number.

[НаджихахНассер]

if we exchange or swap the rows, did we must add -ve sign?

[betoortega]

Professor, good afternoon, I used gaussian elimination an got the followin values:
x= - 22/3, Y= 0, Z = - 1/3, however I tried to solve it by Cramer´s rule and the determinant for the matrix is 0, so it´s not possible to get values for x, y and z.

Could you please help me to understand, why is possible to solve the equation system using gauss and not possible with Cramer´s rule ?

[Evrendogruoglu]

can we say also z free variable, x and y basic variable ?

[philmoseley]

Very good lectures, but it's the usual question - what the hell would I ever need to know this for? What does it achieve other than some weird mental masturbation? Employment for math teachers I suppose.

[fahadkhaledalhemli]

i only understood because of that accent