Answer
0, no inverse.
Work Step by Step
Step 1. List the matrix needed:
$\begin{array} \\A=\\ \end{array}
\begin{bmatrix} 1&0&1&0\\ 0&1&0&1\\1&1&1&2 \\1&2&1&2\end{bmatrix}$
Step 2. Calculate the determinant using row-1 expansion twice (use the formula from section 10.6):
$\begin{array} \\|A|=\\ \end{array}
\begin{vmatrix} 1&0&1\\1&1&2 \\2&1&2\end{vmatrix}+\begin{vmatrix} 0&1&1\\1&1&2 \\1&2&2\end{vmatrix}$
$|A|=1(2-2)+1(1-2)-1(2-2)+1(2-1)=0$
Step 3. Since $det(A)=0$, the matrix does not have an inverse.
