The first is the determinant of a product of matrices. Theorem 3.2.5: Determinant of a Product. Let A and B be two n × n matrices. Then det (AB) = det (A) det (B) In order to find the determinant of a product of matrices, we can simply take the product of the determinants. Consider the following example. Unfortunately this is a mathematical coincidence. It is NOT the case that the determinant of a square matrix is just a sum and difference of all the products of the diagonals. For a 4x4 matrix, you expand across the first column by co-factors, then take the determinant of the resulting 3x3 matrices as above. 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.

I have checked with a matrix calculator and the the determinants of the 3x3 minor matrices are correct. To find the det(B), I multiplied B 14 by det(B 14) and B 24 by det(B 24) and followed the + - + - pattern as showed by the formula here (scroll below for 4x4 formula). The rest will be 0s anyway. det(B)

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
\n \nfinding determinant of 4x4 matrix
This course contains 47 short video lectures by Dr. Bob on basic and advanced concepts from Linear Algebra. He walks you through basic ideas such as how to solve systems of linear equations using row echelon form, row reduction, Gaussian-Jordan elimination, and solving systems of 2 or more equations using determinants, Cramer's rule, and more. I have to find the characteristic polynomial equation of this matrix $$ A= \begin{bmatrix}2 &1 &1&1 \\1&2&1&1\\1&1&2&1\\1&1&1&2 \end{bmatrix}$$ Is 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
\n \n finding determinant of 4x4 matrix
What is the Easiest Way of Finding Determinant of Matrix? Here are some easiest ways/formulas to find the determinant of matrix. The determinant of a 1×1 matrix: If A = [x] 1×1, then |A| = x. The determinant of a 2×2 matrix: If A = \(\left[\begin{array}{cc}a & b \\ \\ c & d\end{array}\right]\) then |A| = ad - bc. JJfv.
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    • finding determinant of 4x4 matrix