Question

(a) Consider the following system of linear equations x1 + x2 + x3 = 9 -x1 - x3 = -8 x2 + x3 = -4 (i) What is the coefficient matrix C of the system? (ii) Calculate det(C) (iii)Does the system have a unique solution

Answer 1

The system's coefficient matrix is [1, 1, 1; -1, 0, -1; 0, 1, 1]. Its determinant equals zero, meaning the system doesn't have a unique solution as the equations are either dependent or inconsistent.

Step-by-step explanation:

To solve the given system of linear equations, we first need to identify the coefficient matrix (C). When we arrange the equations, we get:

x1 + x2 + x3 = 9, -x1 + 0*x2 - x3 = -8, 0*x1 + x2 + x3 = -4

From which the coefficient matrix is:

C = [1, 1, 1; -1, 0, -1; 0, 1, 1]

The determinant of a 3x3 matrix, det(C), is calculated by subtracting the product of the diagonals. This gives:

det(C) = 1*(0*1 - 1*-1) - 1*(-1*1 - -1*0) + 1*(0*-1 - 1*0) = 0

Since the determinant of the coefficient matrix equals zero, the system does not have a unique solution. This is because in a system of linear equations, a zero determinant implies that the equations are either dependent (infinite solutions) or inconsistent (no solutions).

Learn more about Solving System of Linear Equations