Find the Domain 2x-3y+z=0

Problem

2*x−3*y+z=0

Solution

1. Identify the type of equation provided. The equation 2*x−3*y+z=0 represents a linear equation in three variables, which geometrically describes a plane in three-dimensional space ℝ^3

2. Determine the constraints on the variables. In a linear polynomial equation, there are no square roots of negative numbers, no divisions by zero, and no logarithms of non-positive numbers.

3. Conclude the domain. Since the expression is defined for all real values of x y and z that satisfy the equality, the domain of the relation is the set of all ordered triples (x,y,z) in ℝ^3 that lie on the plane. If the task implies finding the domain of z as a function of x and y then x and y can be any real numbers.

Final Answer

Domain={[(x,y,z)∈ℝ^3,2*x−3*y+z=0]}

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