Evaluate the determinants.$\left|\begin{array}{llr}9& 9& 12\\ 4& 4& 6\\ 7& 7& 5\end{array}\right|$

Step by Step Solution: Step 1. We can evaluate this determinant by expanding the first row, the second row, or the third row. Let's expand the first row. Step 2. Using the formula for expanding a 3x3 determinant along the first row, we get:\n$9\left|\begin{array}{cc}4& 6\\ 7& 5\end{array}\right|-9\left|\begin{array}{cc}4& 6\\ 7& 5\end{array}\right|+12\left|\begin{array}{cc}4& 4\\ 7& 7\end{array}\right|$ Step 3. Simplifying, we can see that the first two terms in step 2 are equal, so:\n$9\left|\begin{array}{cc}4& 6\\ 7& 5\end{array}\right|-9\left|\begin{array}{cc}4& 6\\ 7& 5\end{array}\right|+12\left|\begin{array}{cc}4& 4\\ 7& 7\end{array}\right|=12\left|\begin{array}{cc}4& 4\\ 7& 7\end{array}\right|$ Step 4. Using the formula for a 2x2 determinant, we can evaluate the last expression as:\n$12\left|\begin{array}{cc}4& 4\\ 7& 7\end{array}\right|=12[(4)(7)-(4)(7)]=\boxed{0}$ Final Answer: 0