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?

case A)

z = (q+1+2p)/2p

y=2-(2q+2+4p)/2p

x=1

case B) DONT UNDERSTAND

case C) at p = 0 ; q diff than -1

Im soooo confused.. (Headbang) ALL HELP APPRECIATED!

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?

case A)

z = (q+1+2p)/2p

y=2-(2q+2+4p)/2p

x=1

case B) DONT UNDERSTAND

case C) at p = 0 ; q diff than -1

Im soooo confused.. (Headbang) ALL HELP APPRECIATED!

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