Consider the below mentioned 4x4 square matrix or a square matrix of order 4×4, the following changes are to be kept in mind while finding the determinant of a 4×4 matrix: B = \(\left[\begin{array}{cccc}a_{1} & b_{1} & c_{1} & d_{1} \\a_{2} & b_{2} & c_{2} & d_{2} \\a_{3} & b_{3} & c_{3} & d_{3} \\a_{4} & b_{4} & c_{4} & d_{4}\end{array}\right]\)
We can just calculate the determinant of a 4 x 4 matrix using the "conventional" method, i.e. taking the first element of the first row, multiplying it by the determinant of its "augmented" 3 x 3 matrix and so on and so forth. Finding determinant of a 4x4 matrix. I am trying to find the determinant of this matrix but was told by my teacher that we wouldn't need to find the determinant of more than 3 × 3 3 × 3 matrices so I am guessing there is a way of solving this without knowing how to solve a proper 4 × 4 4 × 4 matrix. I think its something to do with the Instead, a better approach is to use the Gauss Elimination method to convert the original matrix into an upper triangular matrix. The determinant of a lower or an upper triangular matrix is simply the product of the diagonal elements. Here we show an example. You seem to have the right ideas. Here's the gist: Any permutation matrix has determinant ±1 ± 1, depending on the parity of the permutation. To find the determinant of an upper triangular or lower triangular matrix, take the product of the diagonal entries. If A = PLU A = P L U, then det(A) = det(P) det(L) det(U) det ( A) = det ( P) det ( L Find determinant of NxN Matrix using recursion: Actual detM = 8, Expected detM = 8 Test Pass: True Matrix 4x4: Actual detM = 20, Expected detM = 20 Test Pass: True Matrix 10x10: Actual detM = 999, Expected detM = 999 Test Pass: True Share. Improve this answer. Follow edited Mar 25, 2022 at 1:41. answered Mar 24
This video explains how to find the inverse matrix of a 4 by 4 matrix using the adjoint method given the determinant and the cofactor matrix.
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