Find the determinant of [[4,8,8],[3,2,9],[3,-1,-6]]: animated lesson

1. 1. The problem
   Worked example

   $\det \begin{bmatrix}4 & 8 & 8 \\ 3 & 2 & 9 \\ 3 & -1 & -6\end{bmatrix}$
2. 2. Step by step
   1. $$A = \begin{bmatrix}4 & 8 & 8 \\ 3 & 2 & 9 \\ 3 & -1 & -6\end{bmatrix}$$
      Read the 3×3 matrix
   2. $$\det A = (4)\begin{vmatrix}2 & 9 \\ -1 & -6\end{vmatrix} - (8)\begin{vmatrix}3 & 9 \\ 3 & -6\end{vmatrix} + (8)\begin{vmatrix}3 & 2 \\ 3 & -1\end{vmatrix}$$
      Expand along the first row (cofactor expansion)
   3. $$M_{11} = -3,\quad M_{12} = -45,\quad M_{13} = -9$$
      Evaluate each 2×2 minor
   4. $$\det A = (4)(-3) - (8)(-45) + (8)(-9) = 276$$
      Combine with the alternating signs + − +
3. 3. The answer
   $$\det A = 276$$

   det = 276

4. 4. Check
   • ✓Computed exactly with fractions; row reduction gives the same value 276.

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