Final answer:
The system of equations is dependent, which means it has an infinite number of solutions. The given matrix represents a multiple of the first equation and does not yield a unique solution for x₁ and x₂.
Step-by-step explanation:
The question asks to solve a system of linear equations using augmented matrix methods. The system given is:
- 3x₁ + 4x₂ = 3
- 9x₁ + 12x₂ = -9
To do this, we first write the augmented matrix representing the system, which is:
\[\begin{bmatrix} 3 & 4 & | & 3 \\ 9 & 12 & | & -9 \end{bmatrix}\]
Then, we use the row reduction method to simplify this matrix into its reduced row echelon form to find the values of x₁ and x₂. However, we notice that the second equation is -3 times the first, which means the system has an infinite number of solutions (it is a dependent system), and we cannot determine unique values for x₁ and x₂ using this matrix.