Introduction To Matrix Operations And Standard Determinants - Sizling People
Home Education Introduction To Matrix Operations And Standard Determinants

Introduction To Matrix Operations And Standard Determinants

A matrix is a rectangular array of numbers arranged in rows and columns. The representation of a matrix is as follows:

matrix representation

An m × n matrix consists of m rows which are horizontal and the n columns which are vertical.

Basic operations of a matrix involve matrix addition, scalar multiplication, transpose, matrix multiplication and row operations. 

OperationDefinitionExample
AdditionThe sum of two matrices A and B is denoted by A + B. It is calculated by adding each element of matrix A to the corresponding element of matrix B and is given by (A + B) = A + B.
Scalar multiplicationWhen a scalar C is multiplied to the matrix A, the product CA is obtained, which is called a scalar product. It is denoted by (CA). It is also called an inner product.
TranspositionThe transpose of a matrix is obtained when the rows and columns are interchanged.

Matrix multiplication is a process of finding the product of two matrices A and B given that 

the number of columns of the left matrix is the same as the number of rows of the right matrix. Suppose A is an m x n matrix and B is an n x p matrix, then the product matrix AB is m x p.

Row operations involve three types, namely:

  • Row addition:  It deals with the addition of two rows.
  • Row multiplication:  It deals with the multiplication of all the numbers of a row by a non-zero constant.
  • Switching of a row is interchanging two rows of a matrix.

The above matrix operations are done while solving linear equations and finding the inverse of a matrix. 

Determinant of a matrix

The determinant det(A) or |A| of a square matrix A is a number that inscribes certain properties of the matrix. The necessary condition for a matrix to be invertible is that its determinant should be nonzero. 

matrix A

Consider a matrix A =

determinant of matrix A

Then

Properties of determinants

The properties of the determinant include the following:

  • There will be a change in the sign if the rows and columns are interchanged.
  • The scalars can be factored out from the rows and columns.
  • There will be no change in the value of the determinant if the multiples of rows and columns are added together.
  • Suppose a row of a matrix is multiplied by a scalar c, then its determinant also gets multiplied by c.
  • The value of a determinant is 0 if a row or a column has zeros in it.
  • The value of a determinant is 0 if two rows or columns are equal.
  • If the elements of the row can be expressed as a sum of two or more elements, then the determinant can be expressed as the sum of two or more determinants.
  • The value of the determinant remains the same even if the equimultiples of corresponding elements of other rows or columns are added to each element of a row or a column of a determinant. 
  • The value of the determinant is equal to the product of diagonal elements if all the elements of a determinant above or below the main diagonal consists of zeros.
  • x – α is a factor of ‘∆’ [value of determinant] if the value of ‘∆’ becomes zero when x = α is substituted.

Standard Determinants

The following are some of the standard determinants:

standard determinants

LEAVE A REPLY

Please enter your comment!
Please enter your name here

Must Read

Key Strategies to deliver a 5-star service every time

The kind of service you may want to deliver depends on your vision for your brand. Give it a moment and think...

Gorgeous Backyard Wedding Decor Ideas for Small Weddings

Host your wedding right in your backyard without missing out on the feeling of extravagance with these cute and creative backyard wedding...

Should B2B Businesses Start Focussing On AI: Experts Talk

Introduction Are you a B2B business owner who is confused about adopting the latest technologies to benefit your company...

Sewing for Beginners: A Basic Guide

Decision made, you want to learn how to sew. Where to begin? Sewing for beginners can be a...

How to Save on Bulk Toilet Paper

If you are interested in doing what's best for your household, you need to always be an intelligent shopper. Even little things...
Download WordPress Themes
Free Download WordPress Themes
Download WordPress Themes
Premium WordPress Themes Download
download udemy paid course for free
download redmi firmware
Premium WordPress Themes Download
ZG93bmxvYWQgbHluZGEgY291cnNlIGZyZWU=