Simul. Linear equations with more than two variables

[panicatthelunchbar]

ok, thanks !

[cltf]

Hi Guys, can someone please help me with these questions. They are from the Essential book. The chapter is just a revision chapter but I don't seem to get the idea of using the parameter/special symbol instead of a numerical value. Why do we have to do this for sim. equations with more than two variables?

5. The system of equations x+y+z+w=4, x+3y+3z=2, x+y+2z−w=6 has infinitely many solutions.
    Describe this family of solutions and give the unique solution when w = 6.

Also, how do you find the inverse of a 3x3 matrix with unknown variables on the CAS and by hand.

Thanks everyone!

You could put the system of equations like this:



~

So I got (x,y,z,w) = (5 - 1.5t,-3 - 1.5t, 2 + 2t, t) (I may be wrong!!!)

As for find the inverse of a 3x3 matrix. If the det =/= 0 then you can find the characteristic polynomial

e.g.

A =

set |A - λI| = 0

So (1 - λ)³ = 0

So

X³ - 3X² + 3X - 1 = 0

So

A³ - 3A² + 3A = I

So

A^-1 = 3I - 3A + A²

Otherwise you can use this row reduction method that takes ages!!!!

So as it turns out, I asked my teacher, since w=6 sub it in. And then everything just falls into place.