Is My Matrix Approach to Solving Linear Equations with Parameters Correct?

[monsmatglad]

Homework Statement

hi. i have a linear equation with parameters that i am trying to solve. unknowns are x, y and z.
(12-3t)x + 2y +2z =2
x +0*y +2z =0
12x + (2-t)y + (2-t)z = 12

i am using a matrix-approach with Gaussian-elimination, and my results (for values of t which allows for a specific solution) seem reasonable, but the the variables depend on t. is this correct, or will the answers be without the parameter t even if t is not specified. i believe i have seen a similar problem in one of my books where the solution is without the parameter t.

Homework Equations

am i getting it wrong?

The Attempt at a Solution

x= -(2t+20)/(3t²t), y= -(37t-110)/(3t²t), z= (t+10)/(3t²t)

 

[BvU]

I think you're doing just fine. For every value of t (*) you have a different set of equations, so it's no wonder t appears in the solution.

(*) for t=0 you get conflicting equations, so it's not surprising there is no answer for x,y,z.

 

[HallsofIvy]

I am puzzled as to why you are writing "$t^2t$" rather than "$t^3$". Am I misunderstanding what you mean?

 

[ehild]

The Attempt at a Solution

x= -(2t+20)/(3t²t), y= -(37t-110)/(3t²t), z= (t+10)/(3t²t)

Check the denominator. I think you just copied it wrong.