Question

Solve the system of equations using the INVERSE and RREF methods. Show appropriate work for each method.

1. X = -6 + 3z
2. 2x + 2z = y + 15
3. 7x - 3y - 5z = 7

Please demonstrate the step-by-step process of solving this system of equations using both the INVERSE and RREF methods.""

Answer 1

To solve the system of equations, transform it into a matrix equation and apply the inverse method by finding the inverse of the coefficient matrix, or the RREF method by reducing the augmented matrix to RREF, both yielding the solution for variables.

Step-by-step explanation:

To solve the system of equations using both the inverse and RREF (Row Reduced Echelon Form) methods, we will treat the given system of equations as a matrix equation A*X = B, and then proceed with the steps for each method.

INVERSE Method Steps:

1. Write the equations in matrix form, A*X = B, where A is the coefficient matrix, X is the variable matrix, and B is the constants matrix.
2. Find the inverse of matrix A, denoted as A-1.
3. Multiply A-1 by B to get X, which contains the solutions for the variables.

RREF Method Steps:

1. Construct the augmented matrix [A|B] using the coefficients and constants of the equations.
2. Use elementary row operations to reduce the augmented matrix to Row Reduced Echelon Form (RREF).
3. The RREF will directly give the solutions for the variables.