Final answer:
The False Position method is a numerical algorithm used to find the roots of a continuous function that changes sign over an interval. The student's question seems to involve performing five iterations of this method within the interval [1,2], yet the provided equation is invalid for such a process. Vector subtraction is referenced, but it's not directly relevant to the False Position method.
Step-by-step explanation:
The subject of the question is concerning the False Position method (or Regula Falsi), which is a numerical method used to find the roots of a function. The student is asked to perform five iterations using this method, given the interval [1,2]. However, the equation provided −4=0 is incorrect as it does not represent a function for which we need to find a root. Normally, the False Position method requires a continuous function that changes sign over an interval [a,b] to apply the iterative steps.
For a valid function f(x), the False Position method would involve taking two points a and b such that f(a) and f(b) have opposite signs and using the formula:
xn = b - f(b) * (b - a) / (f(b) - f(a))
the next approximation to the root is found. This process is repeated until a sufficiently accurate value is reached or a specified number of iterations is completed.
Vector subtraction as exemplified can also be related to the concept of positional adjustments in mathematical operations, though it is not directly connected to the False Position method.