Choose a real-world scenario or context (e.g., population growth, economic trends, or scientific experiment) for your system of linear equations.
Write a system of at least three linear equations that models the scenario.
Write the augmented matrix corresponding to the system of equations you formulated.
Perform Gaussian elimination to transform the augmented matrix to row-echelon
Solve the system and express the solution as an ordered triple.
Perform Cramer’s rule to solve the system and express the solution as an ordered triple.
Interpret the solution in the context of the real-world scenario.
Write a reflection on the process of using matrices Gaussian elimination, and cramer’s rule to solve the system.
Part 2: Matrix Encryption and Decryption
Define a 2×2 square matrix for encryption purposes.
Demonstrate the process of finding the multiplicative inverse of the matrix.
Choose a short message or phrase to encode.
Develop a matrix encoding scheme based on the previously defined matrix.