It's possible to obtain in Wolfram Mathematica the eigenvalues of a 3x3 non-numeric matrix (i.e. a symbolic, expressions only matrix). However, scaling it to a 4x4 matrix does not seem possible
Question: Consider those 4×4 matrices whose entries are all 1 ,-1 , or 0 . What is the maximal value of the determinantof a matrix of this type? Give an example of a matrixwhose determinant has this maximal value. Linear algebra pls explain. Consider those 4 × 4 matrices whose entries are all 1 , - 1 , or 0 .

A Determinant Calculator 4×4 is an online tool that can solve 4×4 order matrices to find out their determinants. It is a very powerful tool, as solving determinants for the 3×3 Matrix is already so difficult. Having to solve the determinant for a 4×4 Order Matrix almost seems impossible by hand. The calculator is very easy and intuitive to use.

The determinant of a matrix product is the product of the determinants: The determinant of the inverse is the reciprocal of the determinant: A matrix and its transpose have equal determinants: The symbol M ij represents the determinant of the matrix that results when row i and column j are eliminated. The following list gives some of the minors from the matrix above. In a 4 x 4 matrix, the minors are determinants of 3 X 3 matrices, and an n x n matrix has minors that are determinants of (n - 1) X (n - 1) matrices. The determinant can be viewed as a function whose input is a square matrix and whose output is a number. If n n is the number of rows and columns in the matrix (remember, we are dealing with square matrices), we can call our matrix an n × n n × n matrix. The simplest square matrix is a 1 × 1 1 × 1 matrix, which isn't very interesting since
The determinant of a square matrix is a single number that, among other things, can be related to the area or volume of a region. In particular, the determinant of a matrix reflects how the linear transformation associated with the matrix can scale or reflect objects. Here we sketch three properties of determinants that can be understood in
Finding determinant of a 2x2 matrix Evalute determinant of a 3x3 matrix; Area of triangle; Equation of line using determinant; Finding Minors and cofactors; Evaluating determinant using minor and co-factor; Find adjoint of a matrix; Finding Inverse of a matrix; Inverse of two matrices and verifying properties
The characteristic polynomial of A is the function f(λ) given by. f(λ) = det (A − λIn). We will see below, Theorem 5.2.2, that the characteristic polynomial is in fact a polynomial. Finding the characterestic polynomial means computing the determinant of the matrix A − λIn, whose entries contain the unknown λ. .
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    • determinant of a 4x4 matrix example