Find the determinant of [[0,2,-4],[8,1,-6],[8,0,-8]]: animated lesson

1. 1. The problem
   Worked example

   $\det \begin{bmatrix}0 & 2 & -4 \\ 8 & 1 & -6 \\ 8 & 0 & -8\end{bmatrix}$
2. 2. Step by step
   1. $$A = \begin{bmatrix}0 & 2 & -4 \\ 8 & 1 & -6 \\ 8 & 0 & -8\end{bmatrix}$$
      Read the 3×3 matrix
   2. $$\det A = (0)\begin{vmatrix}1 & -6 \\ 0 & -8\end{vmatrix} - (2)\begin{vmatrix}8 & -6 \\ 8 & -8\end{vmatrix} + (-4)\begin{vmatrix}8 & 1 \\ 8 & 0\end{vmatrix}$$
      Expand along the first row (cofactor expansion)
   3. $$M_{11} = -8,\quad M_{12} = -16,\quad M_{13} = -8$$
      Evaluate each 2×2 minor
   4. $$\det A = (0)(-8) - (2)(-16) + (-4)(-8) = 64$$
      Combine with the alternating signs + − +
3. 3. The answer
   $$\det A = 64$$

   det = 64

4. 4. Check
   • ✓Computed exactly with fractions; row reduction gives the same value 64.

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