Find the determinant of [[-2,4,7],[8,-5,-1],[0,4,3]]: animated lesson

1. 1. The problem
   Worked example

   $\det \begin{bmatrix}-2 & 4 & 7 \\ 8 & -5 & -1 \\ 0 & 4 & 3\end{bmatrix}$
2. 2. Step by step
   1. $$A = \begin{bmatrix}-2 & 4 & 7 \\ 8 & -5 & -1 \\ 0 & 4 & 3\end{bmatrix}$$
      Read the 3×3 matrix
   2. $$\det A = (-2)\begin{vmatrix}-5 & -1 \\ 4 & 3\end{vmatrix} - (4)\begin{vmatrix}8 & -1 \\ 0 & 3\end{vmatrix} + (7)\begin{vmatrix}8 & -5 \\ 0 & 4\end{vmatrix}$$
      Expand along the first row (cofactor expansion)
   3. $$M_{11} = -11,\quad M_{12} = 24,\quad M_{13} = 32$$
      Evaluate each 2×2 minor
   4. $$\det A = (-2)(-11) - (4)(24) + (7)(32) = 150$$
      Combine with the alternating signs + − +
3. 3. The answer
   $$\det A = 150$$

   det = 150

4. 4. Check
   • ✓Computed exactly with fractions; row reduction gives the same value 150.

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