Kilbaha exam 2 2011 multiple choice question

[Inside Out]

6) px+3y+z=5.       2x-y+2pz=3.        X+4y+pz=6.         Cbs putting alll the choices but basically when is there inf many and no solutions ?

[Panicmode]

6) px+3y+z=5.       2x-y+2pz=3.        X+4y+pz=6.         Cbs putting alll the choices but basically when is there inf many and no solutions ?

This is me solving it via matrix methods (attached). Note; you're not required to know how to solve for the inverse of 3x3 matrices.The trick is to set up a matrix, find the determinant, then set the determinant equal to 0. When solving for the inverse, you have to divide by the determinant. No solutions/infinite solutions exist when the determinant = 0 as one can't divide by 0.

On a cas calc, to find determinant type in the matrix and define it (I define mine as capital letters, eg. A) Then type in det(name of matrix) eg. det(A) and click exe. It will provide you with the determinant.

Once you've solved for p you've got to test which value of p is which by subbing in the values found. On a cas calc, this ca done by using the simultaneous equations function and subbing the respective values for p.

Hope I helped =D