Question

"Convert the following systems into a matrix.

2x – 3y + 7z = 8
x + y - z = 0
-5x + 3y - 5z = 10

Answer 1

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.