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Finding the Determinant of a 2×2 Matrix

Related Topics:
Matrices
Inverse of a 2×2 Matrix
Determinant of a 3×3 Matrix


 

Determinants are useful properties of square matrices, but can involve a lot of computation. A 2×2 determinant is much easier to compute than the determinants of larger matrices, like 3×3 matrices. To find a 2×2 determinant we use a simple formula that uses the entries of the 2×2 matrix. 2×2 determinants can be used to find the area of a parallelogram and to determine invertibility of a 2×2 matrix.

If the determinant of a matrix is 0 then the matrix is singular and it does not have an inverse.


Determinant of a 2×2 Matrix

Before we can find the inverse of a matrix, we need to first learn how to get the determinant of a matrix.

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Example:

Solution:

 

Example:

Solution:


How to find the determinant of a 2×2 matrix, and solve a few related problems?
Examples:
1. Check whether a matrix is singular.
2. Given that the value of the determinant of A is 24, find w.



Explains the formula used to determine the inverse of a 2×2 matrix, if one exists
Two examples of calculating a 2×2 determinant
One example contains fractions.
If det(A) = 0, the matrix is singular. This means it is not invertible or is degenrate and does not have an inverse such that:
AA = I
Further lessons on determinants of matrices
Another video on the determinant of a 2×2 matrix


Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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