# Define determinant. Evaluate without expanding $$\begin{vmatrix}1 & 5 & -6\\ -1 & -4 & 4\\ -2 & -7 & 9\end{vmatrix}$$

The determinant of a matric is a scalar value that is a function of the entries of a square matrix. It is basically a special number that is calculated from a square matric.

$$\begin{vmatrix}1 & 5 & -6\\ -1 & -4 & 4\\ -2 & -7 & 9\end{vmatrix}$$

Apply R2 🡒 R2 + R1, R3 🡒 R3 + R1

~ $$\begin{vmatrix}1 & 5 & -6\\ 0 & 1 & -2\\ 0 & 3 & -3\end{vmatrix}$$

Apply R3 🡒 R3 – 3R2

~ $$\begin{vmatrix}1 & 5 & -6\\ 0 & 1 & -2\\ 0 & 0 & 3\end{vmatrix}$$

Since, it is a upper-triangular matrix

so, Determinant = 1 x 1 x 3 = 3