Convert the system of equations into a matrix equation.
x+4y-z=7
x+y+z=2
-2x-2y+2z=-8
To convert the system of equations into a matrix equation, we need to represent the coefficients of the variables and the constants as matrices.
Let's represent the system of equations using the following variables:
x + 4y - z = 7 -- Equation 1
x + y + z = 2 -- Equation 2
-2x - 2y + 2z = -8 -- Equation 3
To convert this system into a matrix equation, we define the matrices A, X, and B as follows:
Matrix A:
| 1 4 -1 |
| 1 1 1 |
| -2 -2 2 |
Matrix X:
| x |
| y |
| z |
Matrix B:
| 7 |
| 2 |
| -8 |
Now, we can represent the system of equations in matrix form:
Matrix A * Matrix X = Matrix B
To get the matrix equation, the resulting matrix equation will be:
| 1 4 -1 | | x | | 7 |
| 1 1 1 | | y | = | 2 |
| -2 -2 2 | * | z | | -8 |
So, the matrix equation representing the given system of equations is:
| 1 4 -1 | | x | | 7 |
| 1 1 1 | | y | = | 2 |
| -2 -2 2 | * | z | | -8 |
Please note that matrix multiplication is not commutative, so the order of the matrices is important. The order of the matrices in the matrix equation should match the order in the multiplication as shown above.