The correct option is B p≠2,q≠3
Given planes are:
2x+py+6z=8x+2y+qz=5x+y+3z=4
Augmented matrix, A=⎡⎢⎣2p6812q51134⎤⎥⎦
We will find the rank of matrix A. For the planes to intersect in a point, the rank of this matrix must be 3.
R3→R3−12R1 and R2→R2−12R1
A=⎡⎢
⎢⎣2p6802−p2q−3101−p200⎤⎥
⎥⎦
For the given system of equation to have unique solution,
1−p2≠0 and q−3≠0
⇒p≠2 and q≠3