the cartesian equations of 3 planes are:
x + y + z = 3
3x - y - z = 1
x + py = q
By writing down the augmented matrix for this system and reducing it to echelon form,
find for what values of p and q these planes
(a) intersect at a single point;
(b) intersect along a line;
(c) have no common line or point of intersection.
In case (a) find, in terms of p and q, the coordinates of the point, and in case (b) find the scalar parametric equations of the line.
i got the row echelon form to be
1 2 2 | 3
0 1 2 | 2
0 0 2p | q+1+2p
is the above true and if so are these true?
z = (q+1+2p)/2p
case B) DONT UNDERSTAND
case C) at p = 0 ; q diff than -1
Im soooo confused.. ALL HELP APPRECIATED!