Determinant of a 3x3 Matrix
Related Pages
Inverse of a 2×2 Matrix
Inverse Matrix
Determinant of a 2×2 Matrix
Matrices
More Lessons for Grade 9
These lessons, with videos, examples, and solutions, help Algebra students learn how to find the determinant of a 3×3 matrix.
How to calculate the determinant using cofactor expansion?
The minor of an element aij (the element in the i-th row and j-th column) is the determinant of the smaller matrix formed by deleting the i-th row and j-th column of the original matrix.
The cofactor of an element aij is the minor of that element multiplied by (-1)i+j. This means the cofactors alternate in sign.
To find the determinant of a matrix using cofactor expansion, you choose any row or column. Then, you multiply each element in that row or column by its cofactor and add the results.
The following diagram shows how to find the determinant of a 3x3 matrix using Cofactor Expansion. Scroll down the page for more examples and solutions.
Learn to find the determinant of a 2x2 matrix
How to evaluate 2x2 and 3x3 determinants using the diagonal method and cofactor method.
Example of how to calculate the determinant using the diagonal method.
Example of how to calculate the determinant using the diagonal method
Example of how to calculate the determinant using the cofactor method.
Example of how to calculate the determinant using the cofactor method.
Finding the Determinant of a 3×3 matrix.
This video shows the basic formula and compute the determinant of a specific matrix.
3×3 Determinant using the Row Operations Method
Methods for computing a 3×3 determinant are important and are used when defining the cross product. Finding a 3×3 determinant is not as computationally heavy as finding the determinant of a larger square matrix. However, finding this determinant is more complicated than finding a 2x2 determinant. Using methods for simplifying determinants through row operations can make finding the 3x3 determinant much simpler.
The following diagram shows how to evaluate a Determinant using Elementary Row Operations. Scroll down the page for more examples and solutions on how to find the determinant of matrices.
Evaluating a Determinant Using Elementary Row Operations
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