Write the system of equations as an augmented matrix \[ \left\{\begin{aligned} d-2 a-c & =150 \\ a+c & =250 \\ c & =100 \end{aligned}\right. \]

Step 1 ：Given the system of equations: \(\left\{\begin{aligned} d-2 a-c & =150 \ a+c & =250 \ c & =100 \end{aligned}\right.\)

Step 2 ：We can write this system of equations as an augmented matrix. The coefficients of the variables in each equation are placed in rows, and the constants on the right side of the equations are placed in the last column of the matrix. The variables are assumed to be in the order they are presented in the system of equations. In this case, the order is a, c, d.

Step 3 ：The augmented matrix for the given system of equations is \(\boxed{ \begin{bmatrix} -2 & -1 & 1 & 150 \ 1 & 1 & 0 & 250 \ 0 & 1 & 0 & 100 \end{bmatrix} }\)