1. The problem is to find the system of linear equations corresponding to the given augmented matrix: $$\begin{bmatrix}4 & 0 & 0 \\ 7 & -4 & 0 \\ 0 & 3 & 3\end{bmatrix}$$ 2. The augmented matrix represents the coefficients of variables $x_1$, $x_2$, and the constants on the right side of the equations. 3. From the matrix, the system of equations is: $$4x_1 + 0x_2 = 0$$ $$7x_1 - 4x_2 = 0$$ $$0x_1 + 3x_2 = 3$$ 4. Simplify the equations: $$4x_1 = 0$$ $$7x_1 - 4x_2 = 0$$ $$3x_2 = 3$$ 5. Solve for $x_1$ and $x_2$: From the first equation: $$4x_1 = 0 \implies x_1 = \frac{\cancel{4}x_1}{\cancel{4}} = 0$$ From the third equation: $$3x_2 = 3 \implies x_2 = \frac{\cancel{3}x_2}{\cancel{3}} = 1$$ 6. Check the second equation with these values: $$7(0) - 4(1) = 0 - 4 = -4 \neq 0$$ This indicates the system is inconsistent as given, but the system from the matrix is: $$4x_1 = 0$$ $$7x_1 - 4x_2 = 0$$ $$3x_2 = 3$$