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 ℝ3

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 ℝ3 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)∈ℝ3,2*x−3*y+z=0]}

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