Question

Use the inverse of the coefficient matrix to solve the system of equations.

x+2y+3z = 11
2x+3y+4z = -10
−x−4y−8z = −66

Answer 1

(x, y, z) = (-62, 50, -9)

Explanation:

You want the solution to this system of equations using the inverse of the coefficient matrix.

x+2y+3z = 11

2x+3y+4z = -10

−x−4y−8z = −66

Inverse matrix

The inverse of the coefficient matrix is the transpose of the cofactor matrix, divided by the determinant. There are some shortcuts that can be used to make the computation easier. Easiest is letting a calculator find the matrix inverse. (See the first attachment.)

Solution

The solution to the set of equations is the product of the inverse matrix and the constant vector on the right of the equal signs. That, too, can be found using a calculator. (See the second attachment.)

The solution is (x, y, z) = (-62, 50, -9).