PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Expert Solution & Answer
Chapter 7.3, Problem 107E
Solution
a.
To determine: The geometrically how such a system can have a unique solution.
If the three planes intersect at a single point then, exist a unique solution.
Given Information:
Assume that the graph of a linear equation in three variables is a plane in 3-dimensional space.
Explanation:
Consider the given matrix,
Each linear equation in three variables represent a plane in a 3-dimensional space. There is a unique solution if the three planes intersect at a single point as shown:
Each linear equation in three variables represent a plane.
Thus, if the three planes intersect at a single point then, exist a unique solution.
b.
To determine: The geometrically how such a system can be have no solution and describe several possibilities.
There are no solutions if at least 2 planes are parallel.
Given Information:
Assume that the graph of a linear equation in three variables is a plane in 3-dimensional space.
Explanation:
Consider the given information,
Each linear equation in three variables represent a plane in a 3-dimensional space. There are no solutions if at least 2 planes are parallel. Two such cases are shown:
Each linear equation in three variables represent a plane in a 3-dimensional space. There are no solutions if at least 2 planes are parallel. Two such cases are shown:
Each linear equation in three variables represent a plane. There are no solutions if at least 2 planes are parallel.
c.
To determine: The geometrically how such a system can have infinitely many solution and describe several possibilities also make physical models of you find that helpful.
If the planes intersect at a line or if they are the same plane, to name two ways.
Given Information:
Assume that the graph of a linear equation in three variables is a plane in 3-dimensional space.
Explanation:
Consider the given information,
Each linear equation in three variables represent a plane in a 3-dimensional space. There are infinitely many solutions if the planes intersect at a line or if they are the same plane, to name two ways. These first case is shown below:
Each linear equation in three variables represent a plane in a 3-dimensional space.
There are infinitely many solutions if the planes intersect at a line or if they are the same plane, to name two ways.
Chapter 7 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
Ch. 7.1 - Prob. 1QRCh. 7.1 - Prob. 2QRCh. 7.1 - Prob. 3QRCh. 7.1 - Prob. 4QRCh. 7.1 - Prob. 5QRCh. 7.1 - Prob. 6QRCh. 7.1 - Prob. 7QRCh. 7.1 - Prob. 8QRCh. 7.1 - Prob. 9QRCh. 7.1 - Prob. 10QR
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