2. Rango usando determinantes \( \left|\begin{array}{ccc}0 & 2 & -5 \\ 3 & -4 & 1 \\ 6 & 7 & -2\end{array}\right| \)

Calculate or simplify the expression \( \left|\begin{array}{ccc}0 & 2 & -5 \\ 3 & -4 & 1 \\ 6 & 7 & -2\end{array}\right| \). Matrices by following steps: - step0: Solution: \(\left|\begin{array}{cc}{0}&{2}&{-5}\\{3}&{-4}&{1}\\{6}&{7}&{-2}\end{array}\right|\) - step1: Use cofactor expansion along a row: \(0\times \left|\begin{array}{cc}{-4}&{1}\\{7}&{-2}\end{array}\right|-2\times \left|\begin{array}{cc}{3}&{1}\\{6}&{-2}\end{array}\right|-5\times \left|\begin{array}{cc}{3}&{-4}\\{6}&{7}\end{array}\right|\) - step2: Multiply: \(0-2\left(-12\right)-5\times 45\) - step3: Evaluate: \(0-\left(-24\right)-225\) - step4: Rewrite the expression: \(0+24-225\) - step5: Remove 0: \(24-225\) - step6: Subtract the numbers: \(-201\) El determinante de la matriz dada es -201.