Subjects linear algebra

Basic Variables Ac9Af5

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. The problem asks: In basic solution (B), which variables are basic? 2. The system of equations is: $$ \begin{cases} 2x_1 + 3x_2 + s_1 = 27 \\ 4x_1 + 3x_2 + s_2 = 36 \end{cases} $$ 3. A basic solution corresponds to setting non-basic variables to zero and solving for the basic variables. 4. From the table for solution (B): $$x_1 = 0, \quad x_2 = 9, \quad s_1 = 0, \quad s_2 = 9$$ 5. Variables with nonzero values in a basic solution are considered basic variables. 6. Here, $x_2 = 9$ and $s_2 = 9$ are nonzero, so the basic variables are $x_2$ and $s_2$. 7. Variables $x_1$ and $s_1$ are zero, so they are non-basic. **Final answer:** The basic variables in solution (B) are $x_2$ and $s_2$.