Solve the problem.
-Three planes intersect as illustrated below. Is the system consistent, inconsistent, or dependent?
A)inconsistent
B)consistent, dependent
C)consistent, not dependent

Question

Solve the problem.
-Three planes intersect as illustrated below. Is the system consistent, inconsistent, or dependent? 
A)inconsistent 
B)consistent, dependent 
C)consistent, not dependent

Quizplus · Accepted Answer

Since the three planes intersect at a single point, there is a unique solution, meaning the system is consistent. However, since all three planes pass through the same point, they are dependent on each other, making the system dependent. The three planes intersect at a single point, so the system is consistent. However, the fact that they intersect at a single point means that they are dependent, since the third plane can be obtained as a linear combination of the other two planes. Thus, the system is consistent, dependent.

Solve the Problem. -Three Planes Intersect as Illustrated Below. Is the System Consistent