Final answer:
To solve the system of equations using the inverse of the coefficient matrix, you need to first find the coefficient matrix and then find its inverse. After finding the inverse matrix, you can solve the system of equations by multiplying the inverse matrix by the column matrix of constants.
Step-by-step explanation:
To solve the system of equations using the inverse of the coefficient matrix, we need to first find the coefficient matrix. The coefficient matrix is formed by taking the coefficients of the x, y, and z terms and arranging them in a matrix. In this case, the coefficient matrix is:
| 1 2 3 |
| 2 3 4 |
| -1 -2 -4 |
To find the inverse of this matrix, we can use the formula:
A-1 = (1/det(A)) * adj(A)
Where det(A) is the determinant of the coefficient matrix and adj(A) is the adjugate of the matrix. After finding the inverse matrix, we can then solve the system of equations by multiplying the inverse matrix by the column matrix of constants on the right-hand side of the equations.