To calculate the determinant of a specific matrix in R, you can use the "det ()" function. 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 columns and rows are equal. This tutorial explains how to find the determinant of 3x3 using the short trick which is known as triangle's rule and sarrus's rule. Later in this tutorial, 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. 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 This is a 3 by 3 matrix. And now let's evaluate its determinant. So what we have to remember is a checkerboard pattern when we think of 3 by 3 matrices: positive, negative, positive. So first we're going to take positive 1 times 4. So we could just write plus 4 times 4, the determinant of 4 submatrix. It decomposes matrix into two triangular matrices L and U such that A = L*U. L is lower triangular matrix and U is upper triangular matrix. Since A = L*U, then det(A) = det(L)*det(U). Now the fact that determinant of a triangular matrix is equal to product od elements on the diagonal allows to compute det(L) and det(U) easy. Multiply this by -34 (the determinant of the 2x2) to get 1*-34 = -34. 6. Determine the sign of your answer. Next, you'll multiply your answer either by 1 or by -1 to get the cofactor of your chosen element. Which you use depends on where the element was placed in the 3x3 matrix. Find Determinant of 2x2 Matrix; Program in C to read square matrix of order n, find average of elements and then replace each element by 1 if it is greater than average otherwise replace by 0; C Program to find Determinant of Matrix; C Program to Check String Palindrome (No String Function) Longest Word From Given Sentence BQL8llG.