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

1. 1. The problem
   Worked example

   $\det \begin{bmatrix}3 & 1 \\ 4 & 2\end{bmatrix}$
2. 2. Step by step
   1. $$A = \begin{bmatrix}3 & 1 \\ 4 & 2\end{bmatrix}$$
      Read the 2×2 matrix
   2. $$\det A = (3)(2) - (1)(4) = 6 - (4) = 2$$
      Use ad − bc for a 2×2 matrix
3. 3. The answer
   $$\det A = 2$$

   det = 2

4. 4. Check
   • ✓Computed exactly with fractions; row reduction gives the same value 2.

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

• Video lesson

  $\det \begin{bmatrix}-3 & 2 & -5 \\ -7 & -1 & -6 \\ -9 & 2 & 3\end{bmatrix}$

  ▶0:36
  Linear algebraCollege4 steps

  Find the determinant of [[-3,2,-5],[-7,-1,-6],[-9,2,3]]

  Matrices

• Video lesson

  Multiply [[1,2],[3,4]] × [[5,6],[7,8]]

  ▶0:34
  Linear algebraCollege4 steps

  Multiply [[1,2],[3,4]] × [[5,6],[7,8]]

  Matrices

• Video lesson

  $\det \begin{bmatrix}2 & -5 & -5 \\ 4 & -8 & -7 \\ 8 & 1 & 8\end{bmatrix}$

  ▶0:38
  Linear algebraCollege4 steps

  Find the determinant of [[2,-5,-5],[4,-8,-7],[8,1,8]]

  Matrices

• Video lesson

  Calculate 2 × [[1,2],[3,4]]

  ▶0:24
  Linear algebraCollege3 steps

  Calculate 2 × [[1,2],[3,4]]

  Matrices

• Video lesson

  $\det \begin{bmatrix}2 & 8 & -4 \\ 7 & 8 & 0 \\ -9 & -9 & 9\end{bmatrix}$

  ▶0:37
  Linear algebraCollege4 steps

  Find the determinant of [[2,8,-4],[7,8,0],[-9,-9,9]]

  Matrices

• Video lesson

  $\det \begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix}$

  ▶0:28
  Linear algebraCollege2 steps

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

  Matrices

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