Answer:
(a) (-1, 3, 2)
(b) (24, -12, 6)
(c) two planes are identical and parallel to the third
Step-by-step explanation:
You want the point of intersection of the given planes, or the reason why they don't intersect.
Set a)
Using a calculator's matrix row-reduction function, we find the point of intersection to be (-1, 3, 2).
Set b)
Using a calculator's matrix row-reduction function, we find the point of intersection to be (24, -12, 6).
Set c)
Using a calculator's matrix row-reduction function, we find the equations are both dependent and inconsistent. Writing each equation in standard form, we have ...
π1: x -6y +4z = 10
π2: x -6y +4z = 8 . . . . . . parallel to π1, "inconsistent"
π3: x -6y +4z = 10 . . . . . identical to π1
The row 0 0 0 1 in the reduced matrix (2nd attachment) indicates inconsistent equations. The row 0 0 0 0 in the reduced matrix indicates inconsistent equations.
