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

1. 1. The problem
   Worked example

   $\det \begin{bmatrix}2 & -1 & 0 \\ 1 & 3 & 2 \\ 0 & 1 & 4\end{bmatrix}$
2. 2. Step by step
   1. $$A = \begin{bmatrix}2 & -1 & 0 \\ 1 & 3 & 2 \\ 0 & 1 & 4\end{bmatrix}$$
      Read the 3×3 matrix
   2. $$\det A = (2)\begin{vmatrix}3 & 2 \\ 1 & 4\end{vmatrix} - (-1)\begin{vmatrix}1 & 2 \\ 0 & 4\end{vmatrix} + (0)\begin{vmatrix}1 & 3 \\ 0 & 1\end{vmatrix}$$
      Expand along the first row (cofactor expansion)
   3. $$M_{11} = 10,\quad M_{12} = 4,\quad M_{13} = 1$$
      Evaluate each 2×2 minor
   4. $$\det A = (2)(10) - (-1)(4) + (0)(1) = 24$$
      Combine with the alternating signs + − +
3. 3. The answer
   $$\det A = 24$$

   det = 24

4. 4. Check
   • ✓Computed exactly with fractions; row reduction gives the same value 24.

Determinants, inverses, products, transposes and eigenvalues of matrices.

• Video lesson

  Transpose of [[1,2,3],[4,5,6]]

  ▶0:25
  Linear algebraCollege3 steps

  Transpose of [[1,2,3],[4,5,6]]

  Matrices

• Video lesson

  Multiply [[1,2],[3,4]] - [[4,3],[2,1]]

  ▶0:28
  Linear algebraCollege4 steps

  Multiply [[1,2],[3,4]] - [[4,3],[2,1]]

  Matrices

• Video lesson

  $\begin{bmatrix}1 & 2 & 3 \\ 0 & 1 & 4 \\ 5 & 6 & 0\end{bmatrix}^{-1}$

  ▶0:45
  Linear algebraCollege7 steps

  Inverse of [[1,2,3],[0,1,4],[5,6,0]]

  Matrices

• Video lesson

  Find the determinant of [[1,2,0,1],[0,1,3,2],[2,0,1,1],[1,1,1,1]]

  ▶0:53
  Linear algebraCollege6 steps

  Find the determinant of [[1,2,0,1],[0,1,3,2],[2,0,1,1],[1,1,1,1]]

  Matrices

• Video lesson

  Calculate 3 × [[1,-2],[0,4]]

  ▶0:26
  Linear algebraCollege3 steps

  Calculate 3 × [[1,-2],[0,4]]

  Matrices

• Video lesson

  $\det \begin{bmatrix}5 & 7 \\ 2 & 3\end{bmatrix}$

  ▶0:26
  Linear algebraCollege2 steps

  Find the determinant of [[5,7],[2,3]]

  Matrices

• All matrices lessons
• Browse the whole lesson library
• Make a lesson from your own problem
• Step-by-step solver: check your own answer.