Final answer:
To solve the system of equations using the inverse of the coefficient matrix, write the system in matrix form, find the inverse of the coefficient matrix, and multiply both sides of the matrix equation by the inverse.
Step-by-step explanation:
To solve the system of equations using the inverse of the coefficient matrix, we need to write the system in matrix form and find the inverse of the coefficient matrix. Given the system:
8x - y + 7z = 4
6y + 6z = 24
2x + 6y + 4z = 22
We can represent it as:
[8 -1 7] [x] = [4]
[0 6 6] [y] = [24]
[2 6 4] [z] = [22]
Now, we can find the inverse of the coefficient matrix [8 -1 7; 0 6 6; 2 6 4].
Calculating the inverse, we get:
[22/7 -1/7 3/7]
[1/7 0 0]
[-6/7 1/7 -3/7]
Now, multiplying both sides of the matrix equation by the inverse, we get the solution:
[x] = [22/7 -1/7 3/7] [4]
[y] = [1/7 0 0] [24]
[z] = [-6/7 1/7 -3/7] [22]
Simplifying, we find:
x = 22/7
y = 0
z = -6/7Learn more about Solving systems of equations here: