Final Answer:
In solving a system of linear equations, the operation that involves multiplying both sides of the equation by the inverse of the coefficient matrix is (Option A) Matrix Inversion.
Step-by-step explanation:
Matrix inversion is a fundamental operation in solving systems of linear equations. When confronted with a system of equations represented as A*X = B, where A is the coefficient matrix, X is the vector of variables, and B is the constant matrix, multiplying both sides by the inverse of matrix A allows isolating X. This operation is expressed as A^(-1) * A * X = A^(-1) * B, and since A^(-1) * A is the identity matrix I, it simplifies to I * X = A^(-1) * B, resulting in X = A^(-1) * B (Option A).
Mathematically, the inverse of matrix A is denoted as A^(-1), and it exists only for square matrices where the determinant is non-zero. The process of matrix inversion is crucial in solving systems of linear equations efficiently. It allows finding the unique solution vector X by pre-multiplying both sides of the equation by the inverse of the coefficient matrix, effectively canceling out the matrix A and isolating the variable vector X. This method is particularly useful in applications such as engineering, physics, and computer science, where systems of linear equations frequently arise.