From f9052e66b87c2c72621929d5d260318a53e84d5e Mon Sep 17 00:00:00 2001 From: p-murli <31705134+p-murli@users.noreply.github.com> Date: Fri, 28 Jun 2019 07:24:23 +0530 Subject: [PATCH] fix: update determinant article (#28693) expanded the stub article and wrote an article for Determinant of a matrix --- .../determinant-of-a-matrix/index.md | 34 ++++++++++++++++--- 1 file changed, 29 insertions(+), 5 deletions(-) diff --git a/guide/english/mathematics/determinant-of-a-matrix/index.md b/guide/english/mathematics/determinant-of-a-matrix/index.md index e0bedd497f2..6b76bc5f19c 100644 --- a/guide/english/mathematics/determinant-of-a-matrix/index.md +++ b/guide/english/mathematics/determinant-of-a-matrix/index.md @@ -3,13 +3,37 @@ title: Determinant of a Matrix --- ## Determinant of a Matrix -This is a stub. Help our community expand it. - -This quick style guide will help ensure your pull request gets accepted. - +The elements of a square matrix can be used to compute a special value called the determinant. It is denoted by det(A) or |A|. The determinant is only defined for a square matrix, i.e a matrix with identical number of rows and columns. + +The determinant of a 2x2 matrix is the simplest case(a 1x1 matrix is just the number itself). +It is found by multiplying the opposite corners and subtracting them. + +![2x2 determinant](https://wikimedia.org/api/rest_v1/media/math/render/svg/5b2e40d390e1d26039aabee44c7d1d86c8755232) + +Subsequent square matrices are just extensions of a 2x2 matrix and can be easily found by reducing them recursively as 2x2 matrices. The determinant of a 3x3 matrix is given below. + + + +The steps to find the determinant for a 3x3 matrix are: +- Choose a row or column to go along (say the 1st row) +- Multiply 'a' by the 2x2 determinant formed without a's row or column. +- Next do the same with b. Here make sure to multiply this value by -1. You will need to multiply -1 to every alternate element in the row. +- Continue this till you do this for all elements in the row. +- Simplify the expression by finding the individual 2x2 determinants +- The value you obtain is the final value of the determinant of the matrix. + +This method can similarly be applied to any nxn square matrix by breking it down into basic 2x2 matrices and finding their determinants. + +Exercise - Try finding the determinant of the following 3x3 matrix + + + + +Answer = 27 #### More Information: - +https://en.wikipedia.org/wiki/Determinant +https://mathinsight.org/determinant_matrix