Thread: Gauss-Jordan Elimination

Solve the following using Gauss-Jordan elimination:





I keep setting up augmented matrices but I do not know how to get it to reduced-eschelon form at all.

Edit: I worked this out:







Is this correct?

Yes, that is correct! Well, done!
(It took me a moment to figure out where that "r" came from!)

You don't say if you did that by row-reducing the augmented matrix but here's how I did it.

The augmented matrix is


Divide the first row by 2, add the original first row to the second row, and subtract the original first row times 4 from the third row to get


Divide the second row by 7, add the original second row to the third row, and subtract the new second row from the first row to get
.

The fact that the last row consists of all "0"s tells us that we will have an infinite number of solutions. From the first equation, so and so . Now let r= z to get your soltutions.

Bah, forgot to write the for the y part on my paper. And yeah, I meant row-reduced since the following question asks to do it using Gaussian-elimination

Thank you.

And to just check, for Gaussian-elimination it would be: