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
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.../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
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@@ -3,13 +3,37 @@ title: Determinant of a Matrix
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## 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:
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+https://en.wikipedia.org/wiki/Determinant
+https://mathinsight.org/determinant_matrix