Determinant of a 4×4 matrix is a unique number which is calculated using a particular formula. If a matrix order is n x n, then it is a square matrix. Hence, here 4×4 is a square matrix which has four rows and four columns. If A is square matrix then the determinant of matrix A is represented as |A|.
To find the determinant of a 4×4 matrix, we will use the simple method, which we usually use to find the determinant of a 3×3 matrix.
How to calculate determinant of 4×4 matrix?
Before we calculate the determinant of a matrix of order 4, let us first check a few conditions.
- if there is any condition, where determinant could be 0 (for example, the complete row or complete column is 0)
- if factoring out of any row or column is possible.
- If the elements of the matrix are the same but reordered on any column or row.
If any of the three cases given above is met, the corresponding methods for calculating 3×3 determinants are used. We transform a row or a column to fill it with 0, except for one element. The determinant will be equivalent to the product of that element and its cofactor. In this situation, the cofactor is a 3×3 determinant, which is estimated with its particular formula.
For Example:
Also, read:
Solved Examples
Let us solve some examples here.
Example 1:
As we can see in the above example, the elements in third row is all 0. Hence, the value of determinant will be zero.
Example 2:
As we can see here, column C1 and C3 are equal. Therefore, the determinant of the matrix is 0.
Example 3:
As we can see here, second and third rows are proportional to each other. Hence, the determinant of the matrix is 0.
Example 4:
As we can see, there is only one element other than 0 on first column, therefore we will use the general formula using this column. The cofactors of the elements which are 0 are not required to be evaluated because the product of cofactors and the elements will be 0 here.
=4(3-3-27-(27+3+3))
=4×(-60)
= -240
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