Solution Found!
If a, b, and c are distinct numbers, then the following
Chapter , Problem 11E(choose chapter or problem)
If a, b, and c are distinct numbers, then the following system is inconsistent because the graphs of the equations are parallel planes. Show that the set of all least-squares solutions of the system is precisely the plane whose equation is \(x-2 y+5 z=(a+b+c) / 3\).
\(\begin{array}{l}x-2 y+5 z=a \\ x-2 y+5 z=b \\ x-2 y+5 z=c\end{array}\)
Questions & Answers
QUESTION:
If a, b, and c are distinct numbers, then the following system is inconsistent because the graphs of the equations are parallel planes. Show that the set of all least-squares solutions of the system is precisely the plane whose equation is \(x-2 y+5 z=(a+b+c) / 3\).
\(\begin{array}{l}x-2 y+5 z=a \\ x-2 y+5 z=b \\ x-2 y+5 z=c\end{array}\)
ANSWER:Solution 11E
Step 1 of 4
The system of equations is,
This system represents parallel planes. So, it has no solution or inconsistent.
The strategy of solution is to show the set of all least square solutions of the system is
