Find all the eigenvalues and associated eigenvectors for the given matrix: $\begin{bmatrix}5 &1 &-1& 0\\0 & 2 &0 &3\\ 0 & 0 &2 &1 \\0 & 0 &0 &3\end Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge 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 = \(\left[\begin{array}{cccc}a_{1} & b_{1} & c_{1} & d_{1} \\a_{2} & b_{2} & c_{2} & d_{2} \\a_{3} & b_{3} & c_{3} & d_{3} \\a_{4} & b_{4} & c_{4} & d_{4}\end{array}\right]\) 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 I have a matrix and I'm supposed to find the determinant. I chose to use the method of row reduction into echelon form and then multiplication across the diagonal. I row reduce the matrix but the answer I get is not the same as what my calculator says. I've gone over this 5 times now, and I can't find where I'm making a mistake. Determinant of a Matrix The determinant is a special number that can be calculated from a matrix. The matrix has to be square (same number of rows and columns) like this one: 3 8 4 6 A Matrix (This one has 2 Rows and 2 Columns) Let us calculate the determinant of that matrix: 3×6 − 8×4 = 18 − 32 = −14 Easy, hey? Here is another example: Example: BUhgIJa.

finding determinant of 4x4 matrix