As another hint, I will take the same matrix, matrix A and take its determinant again but I will do it using a different technique, either technique is valid so here we saying what is the determinant of the 3X3 Matrix A and we can is we can rewrite first two column so first column right over here we could rewrite it as 4 4 -2 and then the second column right over here we could rewrite it -1 5
Note that if you had to find the determinant of a 4x4 or bigger matrix, the methods shown here do not scale well. The number of computations required grows a lot. A really nice thing to do is to row reduce the matrix to what is called an upper triangular (means all the entries below the main diagonal are zero). The determinant of a matrix is the scalar value or number calculated using a square matrix. The square matrix could be 2×2, 3×3, 4×4, or any type, such as n × n, where the number of column and rows are equal. If S is the set of square matrices, R is the set of numbers (real or complex) and f : S → R is defined by f (A) = k, where A ∈ S
Determinant of a 4×4 matrix is a unique number that is also calculated using a particular formula. If a matrix order is in n x n, then it is a square matrix. So, here 4×4 is a square matrix that has four rows and four columns. If A is a square matrix then the determinant of the matrix A is represented as |A|.
Every time I reduced this to row echelon form, I got $\dfrac{1}{48}$ as the determinant when the actual determinant is $48$. Here are the row operations. The rows that I have highlighted are the ones that change the determinant since we are changing a row by a factor. All the other operations don't change the determinant and we never switch

Determinant of a 4×4 matrix is a unique number that is calculated using a special formula. If a matrix is of order n x n then it is a square matrix. So, here 4×4 is a square matrix having 4 rows and 4 columns. Also for a square matrix A that is of the order , its determinant is written as |A|.

\n \n\n \n\n\n finding determinant of 4x4 matrix
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
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    • finding determinant of 4x4 matrix