La fórmula del determinante de la matriz 3 × 3

La fórmula del determinante de la matriz 3 × 3

The standard formula to find the determinant of a 3 √ó 3 matrix is a break down of smaller 2 √ó 2 determinant problems which are very easy to handle. If you need a refresher, check out my other lesson on how to find the determinant of a 2√ó2. Suppose we are given a square matrix A where,

La fórmula del determinante de la matriz 3 × 3

El determinante de la matriz A se calcula como



La fórmula del determinante de la matriz 3 × 3

Aquí están los puntos principales:


  • Notice that the top row elements namely a, b and c serve as scalar multipliers to a corresponding 2-by-2 matrix.
  • The scalar a is being multiplied to the 2√ó2 matrix of left-over elements created when vertical and horizontal line segments are drawn passing through a.
  • The same process is applied to construct the 2√ó2 matrices for scalar multipliers b and c.

Determinant of 3 x 3 Matrix (animated)

La fórmula del determinante de la matriz 3 × 3

Ejemplos de cómo encontrar el determinante de una matriz de 3 × 3

Ejemplo 1: Find the determinant of the 3√ó3 matrix below.



La fórmula del determinante de la matriz 3 × 3

The set-up below will help you find the correspondence between the generic elements of the formula and the elements of the actual problem.

La fórmula del determinante de la matriz 3 × 3

Applying the formula,


La fórmula del determinante de la matriz 3 × 3 La fórmula del determinante de la matriz 3 × 3

Ejemplo 2: Evaluate the determinant of the 3√ó3 matrix below.


La fórmula del determinante de la matriz 3 × 3

Be very careful when substituting the values into the right places in the formula. Common errors occur when students become careless during the initial step of substitution of values.


In addition, take your time to make sure your arithmetic is also correct. Otherwise, a single error somewhere in the calculation will yield a wrong answer in the end.

Ya que,

La fórmula del determinante de la matriz 3 × 3

our calculation of the determinant becomes…

La fórmula del determinante de la matriz 3 × 3 La fórmula del determinante de la matriz 3 × 3

Ejemplo 3: Solve for the determinant of the 3√ó3 matrix below.

La fórmula del determinante de la matriz 3 × 3

The presence of zero (0) in the first row should make our computation much easier. Remember, those elements in the first row, act as scalar multipliers. Therefore, zero multiplied to anything will result in the entire expression to disappear.

Here’s the setup again to show the corresponding numerical value of each variable in the formula.

La fórmula del determinante de la matriz 3 × 3

Using the formula, we have…

La fórmula del determinante de la matriz 3 × 3 La fórmula del determinante de la matriz 3 × 3

Practica con hojas de trabajo

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Determinantes de una matriz de 2 √ó 2



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