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 7.3, Problem 106E

Chapter 7.3, Problem 108E

Chapter 7 Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. 7.1 - Prob. 1QR Ch. 7.1 - Prob. 2QR Ch. 7.1 - Prob. 3QR Ch. 7.1 - Prob. 4QR Ch. 7.1 - Prob. 5QR Ch. 7.1 - Prob. 6QR Ch. 7.1 - Prob. 7QR Ch. 7.1 - Prob. 8QR Ch. 7.1 - Prob. 9QR Ch. 7.1 - Prob. 10QR

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - Prob. 15E Ch. 7.1 - Prob. 16E Ch. 7.1 - Prob. 17E Ch. 7.1 - Prob. 18E Ch. 7.1 - Prob. 19E Ch. 7.1 - Prob. 20E Ch. 7.1 - Prob. 21E Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Prob. 24E Ch. 7.1 - Prob. 25E Ch. 7.1 - Prob. 26E Ch. 7.1 - Prob. 27E Ch. 7.1 - Prob. 28E Ch. 7.1 - Prob. 29E Ch. 7.1 - Prob. 30E Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Prob. 34E Ch. 7.1 - Prob. 35E Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Prob. 39E Ch. 7.1 - Prob. 40E Ch. 7.1 - Prob. 41E Ch. 7.1 - Prob. 42E Ch. 7.1 - Prob. 43E Ch. 7.1 - Prob. 44E Ch. 7.1 - Prob. 45E Ch. 7.1 - Prob. 46E Ch. 7.1 - Prob. 47E Ch. 7.1 - Prob. 48E Ch. 7.1 - Prob. 49E Ch. 7.1 - Prob. 50E Ch. 7.1 - Prob. 51E Ch. 7.1 - Prob. 52E Ch. 7.1 - Prob. 53E Ch. 7.1 - Prob. 54E Ch. 7.1 - Prob. 55E Ch. 7.1 - Prob. 56E Ch. 7.1 - Prob. 57E Ch. 7.1 - Prob. 58E Ch. 7.1 - Prob. 59E Ch. 7.1 - Prob. 60E Ch. 7.1 - Prob. 61E Ch. 7.1 - Prob. 62E Ch. 7.1 - Prob. 63E Ch. 7.1 - Prob. 64E Ch. 7.1 - Prob. 65E Ch. 7.1 - Prob. 66E Ch. 7.1 - Prob. 67E Ch. 7.1 - Prob. 68E Ch. 7.1 - Prob. 69E Ch. 7.1 - Prob. 70E Ch. 7.2 - Prob. 1QR Ch. 7.2 - Prob. 2QR Ch. 7.2 - Prob. 3QR Ch. 7.2 - Prob. 4QR Ch. 7.2 - Prob. 5QR Ch. 7.2 - Prob. 6QR Ch. 7.2 - Prob. 7QR Ch. 7.2 - Prob. 8QR Ch. 7.2 - Prob. 9QR Ch. 7.2 - Prob. 10QR Ch. 7.2 - Prob. 1E Ch. 7.2 - Prob. 2E Ch. 7.2 - Prob. 3E Ch. 7.2 - Prob. 4E Ch. 7.2 - Prob. 5E Ch. 7.2 - Prob. 6E Ch. 7.2 - Prob. 7E Ch. 7.2 - Prob. 8E Ch. 7.2 - Prob. 9E Ch. 7.2 - Prob. 10E Ch. 7.2 - Prob. 11E Ch. 7.2 - Prob. 12E Ch. 7.2 - Prob. 13E Ch. 7.2 - Prob. 14E Ch. 7.2 - Prob. 15E Ch. 7.2 - Prob. 16E Ch. 7.2 - Prob. 17E Ch. 7.2 - Prob. 18E Ch. 7.2 - Prob. 19E Ch. 7.2 - Prob. 20E Ch. 7.2 - Prob. 21E Ch. 7.2 - Prob. 22E Ch. 7.2 - Prob. 23E Ch. 7.2 - Prob. 24E Ch. 7.2 - Prob. 25E Ch. 7.2 - Prob. 26E Ch. 7.2 - Prob. 27E Ch. 7.2 - Prob. 28E Ch. 7.2 - Prob. 29E Ch. 7.2 - Prob. 30E Ch. 7.2 - Prob. 31E Ch. 7.2 - Prob. 32E Ch. 7.2 - Prob. 33E Ch. 7.2 - Prob. 34E Ch. 7.2 - Prob. 35E Ch. 7.2 - Prob. 36E Ch. 7.2 - Prob. 37E Ch. 7.2 - Prob. 38E Ch. 7.2 - Prob. 39E Ch. 7.2 - Prob. 40E Ch. 7.2 - Prob. 41E Ch. 7.2 - Prob. 42E Ch. 7.2 - Prob. 43E Ch. 7.2 - Prob. 44E Ch. 7.2 - Prob. 45E Ch. 7.2 - Prob. 46E Ch. 7.2 - Prob. 47E Ch. 7.2 - Prob. 48E Ch. 7.2 - Prob. 49E Ch. 7.2 - Prob. 50E Ch. 7.2 - Prob. 51E Ch. 7.2 - Prob. 52E Ch. 7.2 - Prob. 53E Ch. 7.2 - Prob. 54E Ch. 7.2 - Prob. 55E Ch. 7.2 - Prob. 56E Ch. 7.2 - Prob. 57E Ch. 7.2 - Prob. 58E Ch. 7.2 - Prob. 59E Ch. 7.2 - Prob. 60E Ch. 7.2 - Prob. 61E Ch. 7.2 - Prob. 62E Ch. 7.2 - Prob. 63E Ch. 7.2 - Prob. 64E Ch. 7.2 - Prob. 65E Ch. 7.2 - Prob. 66E Ch. 7.2 - Prob. 67E Ch. 7.2 - Prob. 68E Ch. 7.2 - Prob. 69E Ch. 7.2 - Prob. 70E Ch. 7.2 - Prob. 71E Ch. 7.2 - Prob. 72E Ch. 7.2 - Prob. 73E Ch. 7.3 - Prob. 1QR Ch. 7.3 - Prob. 2QR Ch. 7.3 - Prob. 3QR Ch. 7.3 - Prob. 4QR Ch. 7.3 - Prob. 5QR Ch. 7.3 - Prob. 6QR Ch. 7.3 - Prob. 7QR Ch. 7.3 - Prob. 8QR Ch. 7.3 - Prob. 9QR Ch. 7.3 - Prob. 10QR Ch. 7.3 - Prob. 1E Ch. 7.3 - Prob. 2E Ch. 7.3 - Prob. 3E Ch. 7.3 - Prob. 4E Ch. 7.3 - Prob. 5E Ch. 7.3 - Prob. 6E Ch. 7.3 - Prob. 7E Ch. 7.3 - Prob. 8E Ch. 7.3 - Prob. 9E Ch. 7.3 - Prob. 10E Ch. 7.3 - Prob. 11E Ch. 7.3 - Prob. 12E Ch. 7.3 - Prob. 13E Ch. 7.3 - Prob. 14E Ch. 7.3 - Prob. 15E Ch. 7.3 - Prob. 16E Ch. 7.3 - Prob. 17E Ch. 7.3 - Prob. 18E Ch. 7.3 - Prob. 19E Ch. 7.3 - Prob. 20E Ch. 7.3 - Prob. 21E Ch. 7.3 - Prob. 22E Ch. 7.3 - Prob. 23E Ch. 7.3 - Prob. 24E Ch. 7.3 - Prob. 25E Ch. 7.3 - Prob. 26E Ch. 7.3 - Prob. 27E Ch. 7.3 - Prob. 28E Ch. 7.3 - Prob. 29E Ch. 7.3 - Prob. 30E Ch. 7.3 - Prob. 31E Ch. 7.3 - Prob. 32E Ch. 7.3 - Prob. 33E Ch. 7.3 - Prob. 34E Ch. 7.3 - Prob. 35E Ch. 7.3 - Prob. 36E Ch. 7.3 - Prob. 37E Ch. 7.3 - Prob. 38E Ch. 7.3 - Prob. 39E Ch. 7.3 - Prob. 40E Ch. 7.3 - Prob. 41E Ch. 7.3 - Prob. 42E Ch. 7.3 - Prob. 43E Ch. 7.3 - Prob. 44E Ch. 7.3 - Prob. 45E Ch. 7.3 - Prob. 46E Ch. 7.3 - Prob. 47E Ch. 7.3 - Prob. 48E Ch. 7.3 - Prob. 49E Ch. 7.3 - Prob. 50E Ch. 7.3 - Prob. 51E Ch. 7.3 - Prob. 52E Ch. 7.3 - Prob. 53E Ch. 7.3 - Prob. 54E Ch. 7.3 - Prob. 55E Ch. 7.3 - Prob. 56E Ch. 7.3 - Prob. 57E Ch. 7.3 - Prob. 58E Ch. 7.3 - Prob. 59E Ch. 7.3 - Prob. 60E Ch. 7.3 - Prob. 61E Ch. 7.3 - Prob. 62E Ch. 7.3 - Prob. 63E Ch. 7.3 - Prob. 64E Ch. 7.3 - Prob. 65E Ch. 7.3 - Prob. 66E Ch. 7.3 - Prob. 67E Ch. 7.3 - Prob. 68E Ch. 7.3 - Prob. 69E Ch. 7.3 - Prob. 70E Ch. 7.3 - Prob. 71E Ch. 7.3 - Prob. 72E Ch. 7.3 - Prob. 73E Ch. 7.3 - Prob. 74E Ch. 7.3 - Prob. 75E Ch. 7.3 - Prob. 76E Ch. 7.3 - Prob. 77E Ch. 7.3 - Prob. 78E Ch. 7.3 - Prob. 79E Ch. 7.3 - Prob. 80E Ch. 7.3 - Prob. 81E Ch. 7.3 - Prob. 82E Ch. 7.3 - Prob. 83E Ch. 7.3 - Prob. 84E Ch. 7.3 - Prob. 85E Ch. 7.3 - Prob. 86E Ch. 7.3 - Prob. 87E Ch. 7.3 - Prob. 88E Ch. 7.3 - Prob. 89E Ch. 7.3 - Prob. 90E Ch. 7.3 - Prob. 91E Ch. 7.3 - Prob. 92E Ch. 7.3 - Prob. 93E Ch. 7.3 - Prob. 94E Ch. 7.3 - Prob. 95E Ch. 7.3 - Prob. 96E Ch. 7.3 - Prob. 97E Ch. 7.3 - Prob. 98E Ch. 7.3 - Prob. 99E Ch. 7.3 - Prob. 100E Ch. 7.3 - Prob. 101E Ch. 7.3 - Prob. 102E Ch. 7.3 - Prob. 103E Ch. 7.3 - Prob. 104E Ch. 7.3 - Prob. 105E Ch. 7.3 - Prob. 106E Ch. 7.3 - Prob. 107E Ch. 7.3 - Prob. 108E Ch. 7.3 - Prob. 109E Ch. 7.3 - Prob. 110E Ch. 7.4 - Prob. 1QR Ch. 7.4 - Prob. 2QR Ch. 7.4 - Prob. 3QR Ch. 7.4 - Prob. 4QR Ch. 7.4 - Prob. 5QR Ch. 7.4 - Prob. 6QR Ch. 7.4 - Prob. 7QR Ch. 7.4 - Prob. 8QR Ch. 7.4 - Prob. 9QR Ch. 7.4 - Prob. 10QR Ch. 7.4 - Prob. 1E Ch. 7.4 - Prob. 2E Ch. 7.4 - Prob. 3E Ch. 7.4 - Prob. 4E Ch. 7.4 - Prob. 5E Ch. 7.4 - Prob. 6E Ch. 7.4 - Prob. 7E Ch. 7.4 - Prob. 8E Ch. 7.4 - Prob. 9E Ch. 7.4 - Prob. 10E Ch. 7.4 - Prob. 11E Ch. 7.4 - Prob. 12E Ch. 7.4 - Prob. 13E Ch. 7.4 - Prob. 14E Ch. 7.4 - Prob. 15E Ch. 7.4 - Prob. 16E Ch. 7.4 - Prob. 17E Ch. 7.4 - Prob. 18E Ch. 7.4 - Prob. 19E Ch. 7.4 - Prob. 20E Ch. 7.4 - Prob. 21E Ch. 7.4 - Prob. 22E Ch. 7.4 - Prob. 23E Ch. 7.4 - Prob. 24E Ch. 7.4 - Prob. 25E Ch. 7.4 - Prob. 26E Ch. 7.4 - Prob. 27E Ch. 7.4 - Prob. 28E Ch. 7.4 - Prob. 29E Ch. 7.4 - Prob. 30E Ch. 7.4 - Prob. 31E Ch. 7.4 - Prob. 32E Ch. 7.4 - Prob. 33E Ch. 7.4 - Prob. 34E Ch. 7.4 - Prob. 35E Ch. 7.4 - Prob. 36E Ch. 7.4 - Prob. 37E Ch. 7.4 - Prob. 38E Ch. 7.4 - Prob. 39E Ch. 7.4 - Prob. 40E Ch. 7.4 - Prob. 41E Ch. 7.4 - Prob. 42E Ch. 7.4 - Prob. 43E Ch. 7.4 - Prob. 44E Ch. 7.4 - Prob. 45E Ch. 7.4 - Prob. 46E Ch. 7.4 - Prob. 47E Ch. 7.4 - Prob. 48E Ch. 7.4 - Prob. 49E Ch. 7.4 - Prob. 50E Ch. 7.4 - Prob. 51E Ch. 7.4 - Prob. 52E Ch. 7 - Prob. 1RE Ch. 7 - Prob. 2RE Ch. 7 - Prob. 3RE Ch. 7 - Prob. 4RE Ch. 7 - Prob. 5RE Ch. 7 - Prob. 6RE Ch. 7 - Prob. 7RE Ch. 7 - Prob. 8RE Ch. 7 - Prob. 9RE Ch. 7 - Prob. 10RE Ch. 7 - Prob. 11RE Ch. 7 - Prob. 12RE Ch. 7 - Prob. 13RE Ch. 7 - Prob. 14RE Ch. 7 - Prob. 15RE Ch. 7 - Prob. 16RE Ch. 7 - Prob. 17RE Ch. 7 - Prob. 18RE Ch. 7 - Prob. 19RE Ch. 7 - Prob. 20RE Ch. 7 - Prob. 21RE Ch. 7 - Prob. 22RE Ch. 7 - Prob. 23RE Ch. 7 - Prob. 24RE Ch. 7 - Prob. 25RE Ch. 7 - Prob. 26RE Ch. 7 - Prob. 27RE Ch. 7 - Prob. 28RE Ch. 7 - Prob. 29RE Ch. 7 - Prob. 30RE Ch. 7 - Prob. 31RE Ch. 7 - Prob. 32RE Ch. 7 - Prob. 33RE Ch. 7 - Prob. 34RE Ch. 7 - Prob. 35RE Ch. 7 - Prob. 36RE Ch. 7 - Prob. 37RE Ch. 7 - Prob. 38RE Ch. 7 - Prob. 39RE Ch. 7 - Prob. 40RE Ch. 7 - Prob. 41RE Ch. 7 - Prob. 42RE Ch. 7 - Prob. 43RE Ch. 7 - Prob. 44RE Ch. 7 - Prob. 45RE Ch. 7 - Prob. 46RE Ch. 7 - Prob. 47RE Ch. 7 - Prob. 48RE Ch. 7 - Prob. 49RE Ch. 7 - Prob. 50RE Ch. 7 - Prob. 51RE Ch. 7 - Prob. 52RE Ch. 7 - Prob. 53RE Ch. 7 - Prob. 54RE Ch. 7 - Prob. 55RE Ch. 7 - Prob. 56RE Ch. 7 - Prob. 57RE Ch. 7 - Prob. 58RE Ch. 7 - Prob. 59RE Ch. 7 - Prob. 60RE Ch. 7 - Prob. 61RE Ch. 7 - Prob. 62RE Ch. 7 - Prob. 63RE Ch. 7 - Prob. 64RE Ch. 7 - Prob. 65RE Ch. 7 - Prob. 66RE Ch. 7 - Prob. 67RE Ch. 7 - Prob. 68RE Ch. 7 - Prob. 69RE Ch. 7 - Prob. 70RE Ch. 7 - Prob. 71RE Ch. 7 - Prob. 72RE Ch. 7 - Prob. 73RE Ch. 7 - Prob. 74RE Ch. 7 - Prob. 75RE Ch. 7 - Prob. 76RE Ch. 7 - Prob. 77RE Ch. 7 - Prob. 78RE Ch. 7 - Prob. 79RE Ch. 7 - Prob. 80RE Ch. 7 - Prob. 81RE

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