Question

Given the following augmented matrix, find the solutions to the system of equations that it represents.

[1 8 | 24]
[0 0 | 3]

Answer 1

The given augmented matrix represents an inconsistent system of equations with no solution. The second row of the matrix [0 0 | 3] shows an impossible equation, which indicates the inconsistency.

Step-by-step explanation:

When we look at the given augmented matrix and try to interpret it in terms of a system of equations, it represents two linear equations. The matrix:

[1 8 | 24]
[0 0 | 3]

corresponds to the equations:

• x + 8y = 24
• 0x + 0y = 3

However, there is an inconsistency in this system. The second row, [0 0 | 3], represents the impossible equation 0 = 3, which has no solution. This means the system of equations is inconsistent, and there are no solutions to this system.