From 3a0974f7e7ae4535e24adb65f39ae38177ceb865 Mon Sep 17 00:00:00 2001 From: Sudhakar Kumar Date: Sat, 20 Oct 2018 02:10:10 +0530 Subject: [PATCH] Fix punctuation marks and articles (#20274) --- guide/english/mathematics/2-by-2-determinants/index.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/guide/english/mathematics/2-by-2-determinants/index.md b/guide/english/mathematics/2-by-2-determinants/index.md index 7fc397bf0a..e45ad49786 100644 --- a/guide/english/mathematics/2-by-2-determinants/index.md +++ b/guide/english/mathematics/2-by-2-determinants/index.md @@ -4,7 +4,7 @@ title: 2 by 2 Determinants ## 2 by 2 Determinants -In linear algebra, the determinant of a two-by-two matrix is a useful quantity.Mostly it is used to calculate the area of the given quadilateral(convex polygons only) and is also a easy representation of a quadilateral(convex polygons only) to be stored in computers as arrays. Scientists, engineers, and mathematicians use determinants in many everyday applications including image and graphic processing. +In linear algebra, the determinant of a two-by-two matrix is a useful quantity. Mostly it is used to calculate the area of the given quadilateral (convex polygons only) and is also an easy representation of a quadilateral(convex polygons only) to be stored in computers as arrays. Scientists, engineers, and mathematicians use determinants in many everyday applications including image and graphic processing. Calculating the determinant of a square two-by-two matrix is simple, and is the basis of the [Laplace formula](https://en.wikipedia.org/wiki/Laplace_expansion) used for calculating determinants for larger square matrices. @@ -14,7 +14,7 @@ Given a matrix A, the determinant of A (written as |A|) is given by the followin The rows and vectors of a 2 by 2 matrix can be associated with points on a cartesian plane, such that each row forms a 2D vector. These two vectors form a parallelogram, as shown in the image below. PROOF: -Let the vectors be M(a,b),N(c,d) originating from origin in a 2-D plane with an angle (*theta*>0) between them(head of one vector touching tail of another vector) . But in here it doesn't matter because sin(theta)=sin(2(pi)-theta).Then the other point is P(a+c,b+d).The area of the parallelogram is perpendicular distance from one point say N(c,d) to the base vector, M(a,b) multiplied by the length of the base vector, |M(a,b)|. The parallelogram consists of two triangles hence, the area is two times of a triangle. +Let the vectors be M(a,b),N(c,d) originating from origin in a 2-D plane with an angle (*theta*>0) between them(head of one vector touching tail of another vector). But in here it doesn't matter because sin(theta)=sin(2(pi)-theta). Then the other point is P(a+c,b+d). The area of the parallelogram is perpendicular distance from one point say N(c,d) to the base vector, M(a,b) multiplied by the length of the base vector, |M(a,b)|. The parallelogram consists of two triangles hence, the area is two times of a triangle. Let the perpendicular distance be h h=|N(c,d)|* sin(*theta*(angle between two vectors)) b=|M(a,b)|