Final answer:
To convert the system of equations into a matrix, organize the coefficients of the variables and the constants into an augmented matrix. For the given equations, the matrix form is an augmented matrix [[2, -3, 7, 8], [1, 1, -1, 0], [-5, 3, -5, 10]].
Step-by-step explanation:
To convert the given system of equations into a matrix, we can represent the coefficients of the variables and the constants from each equation in a matrix form. The system of equations:
- 2x – 3y + 7z = 8
- x + y - z = 0
- –5x + 3y - 5z = 10
Can be represented in matrix form as:
A = [[2, -3, 7], [1, 1, -1], [-5, 3, -5]]
b = [8, 0, 10]
So the augmented matrix (A|b) would be:
[[2, -3, 7, 8], [1, 1, -1, 0], [-5, 3, -5, 10]]
This is now in the form Ax = b where A is the coefficient matrix, x is the variable matrix (x, y, z), and b is the constants matrix.