In R, the global environment interacts with other environments in such a way that variables defined in the global environment can be accessed and modified from within functions. This allows functions to utilize global variables as needed. However, variables defined within functions are not automatically added to the global environment, and changes made to global variables within functions may not persist outside of the function's execution.

All the options are valid methods to extract a specific pattern from strings in R. grep() and sub() functions from base R, and str_extract() function from stringr package could be used, depending on the exact requirements of the task.

You would need to use a while loop in R when dealing with an iterative algorithm that requires repetitive execution until a specific condition is met. Iterative algorithms, such as Newton's method for finding roots or gradient descent for optimization, involve repeated calculations and updates until a convergence criterion is satisfied. While loops are useful for implementing such iterative procedures.

All of the mentioned scenarios may require finding the maximum or minimum value in a matrix in R. For example, calculating the peak performance of a computer system may involve analyzing matrix data representing system metrics. Determining the highest and lowest temperature recorded in a dataset requires finding the maximum and minimum values in a temperature matrix. Analyzing the maximum and minimum stock prices over a period involves working with matrices representing stock price data.

In R, a function is defined using the function keyword, followed by the function name, input parameters (if any), and the function body enclosed in curly braces {}. The function body contains the code that defines the operations to be performed by the function.

The syntax for a for loop in R is for (value in sequence) { statements }. The statements inside the curly braces will be executed for each value in the sequence during each iteration of the loop.

In R, to print a string or a message, the print() function is used. For instance, the syntax print("Hello, world!") will display the message "Hello, world!".

A scenario where you would use a nested if statement in R is when you need to evaluate multiple conditions and perform different actions based on each condition. Nested if statements allow you to create more complex branching logic by evaluating multiple conditions within the same code block.

The 'exists()' function in R is used to check if a variable or a function exists in the current environment. This can be useful in debugging, to avoid errors when trying to use a non-existent variable or function.

We would use as.numeric() function to convert character data type to numeric. However, it's important to ensure that the character data is indeed convertible to numeric, otherwise NA's might be introduced.