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

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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

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