Using Matrices

posted on: 14 May, 2012 | updated on: 07 Sep, 2012

Matrices are a Set of Numbers or we can say it is a collection of number which is arranged in rows and column. The numbers which we are using in matrices are Real Numbers. Generally in the matrices the complex numbers are used. With the help of matrices we can solve many problems. Here we will focus on Area of Triangle by using matrices.
We can find the area of triangle by using matrices, which is one of the major applications of matrices.
Now we see how to find the area of a triangle using matrices?
We have to follow some steps for finding the area of triangle by use of matrices:
Step1: First we take a triangle.
Step2: Then we find all the coordinates of vertices of a triangle.
Step3: Then we put all the coordinates in the matrices form and then solve Using Matrices to find the coordinates of a triangle.
We know that the area of triangle is:
Area of triangle = ½ | p₁ q₁ 1|
                                     | p₂ q₂ 1|
                                     | p₃ q₃ 1|
Now we see how to find the area of a triangle using matrices:
Suppose we have the values of vertices of triangle are: (2, 3), (4, 2), (3, 7), here we have to find the area of triangle using matrices method.
For finding the area of triangle using matrices we have to follow above steps:
We know that the vertices of a triangle are:
     (p₁, q₁), (p₂, q₂) and (p₃, q₃).
Step1: First we have triangle coordinates are: (2, 3), (4, 2), (3, 7);
Step2: Now put these coordinates in the given formula:
And we know that the area of triangle is:
Area of triangle = ½ | p₁ q₁ 1|
                                    | p₂ q₂ 1|
                                    | p₃ q₃ 1|
Now putting the value of all coordinates in the given formula:
Area of triangle = ½| 2 3 1|
                                   | 4 2 1|
                                   | 3 7 1|
Now we have to solve the determinant values:
Area of triangle = ½ [2(2 – 7) - 3(4 – 3) + 1(28 – 6)];
Area of triangle = ½ [2(-5) – 3(1) + 1(22)];
Area of triangle = ½ [-10 - 3 + 22];
Area of triangle = ½ [-13 + 22];
Area of triangle = ½[9].
Area of triangle = 4.5 Square inch.
So we get area of triangle equals to 4.5 by using matrices.

Topics Covered in Using Matrices

Augmented Matrices

posted on: 26 Jul, 2012 | updated on: 30 Aug, 2012

Gaussian elimination method is completely based on the need of making augmented matrices for a system of Linear Equations. A matrix is said to be augmented if it represents both right and left parts of equation.
Rows and columns of an augmented matrix represent the equations and coefficients of variables in each column respectively. We don’t write variables in matrix...Read More

Matrix Row Operations

posted on: 18 Aug, 2012 | updated on: 20 Aug, 2012

Matrix is a 2 dimensional array which is used to store elements. One part is called as row and other is column. Elementary matrix is different from identity matrix. We can perform matrix row operations and matrix column operations. Here we will discuss matrix row operation.

Using single elementary matrices row operations we can change a matrix from identity matr...Read More

Identity and Inverse Matrices

posted on: 18 Aug, 2012 | updated on: 20 Aug, 2012

Matrix is made of rows and columns, these rows and columns contain elements. If number of rows and columns are same in a matrix then matrix is a Square matrix. Number of rows and column can be different as well. Now let us discuss identity matrices and inverse matrices.
Now let us discuss these matrices separately,
Identity matrix: Identity matrix is a sq...Read More

Matrices and Determinants

posted on: 18 Aug, 2012 | updated on: 07 Sep, 2012

Matrix is an array which contains elements Numbers in form of rows and columns. Rows and columns are two aspects of a matrix. Let us discuss more about matrices and determinants:

Order of a matrix is represented by number of rows and columns. For Example: If a matrix has 3 rows and 2 columns then order of matrix will be 3 x 2 or we can denote the order of ma...Read More

Using Inverse Matrices

posted on: 20 Aug, 2012 | updated on: 21 Aug, 2012

Matrix is a Set of Numbers in an ordered manner; it is comprised of rows and columns. Matrix A (m, n) indicates that it has ‘m’ number of rows and ‘n’ number of columns. For instance, matrix A (3, 2) represents three rows and two columns.
If there are two matrices A and B then matrix 'A' will be called as inverse matrix if following relationship exists between bo...Read More

Multiplying Matrices

posted on: 30 Aug, 2012 | updated on: 31 Aug, 2012

Matrix is defined as arrangement or different Numbers or variables or even characters. Thus, it is a Combination of constants or a combination of variables. This block is represented in format of rows and columns. Matrix may also be termed as an arrangement of two dimensional matrices. Various operations can be performed over matrices such as addition of matrices, s...Read More

An Introduction to Matrices

posted on: 25 May, 2012 | updated on: 20 Aug, 2012

Matrix can be defined as collection of Numbers. These numbers are ordered in rows and columns. As an introduction to matrices we can say that a matrix is a 2- dimensional array which has rows and columns to represent elements.
In matrix we denote rows by ‘i’ and column by ‘j’. We can calculate the order of matrices by number of rows and columns. For Example:...Read More