top of page
Search

# What you need to know about Determinant of a Matrix - Class 12 Mathematics

Updated: Feb 25

Once upon a time, there were two friends Sarah and John, who were enthusiastic about Mathematics. They were both in Grade 12 and their Math teacher Mr. Smith had just introduced Matrices and Determinants. One sunny afternoon, after school, Sarah and John decided to explore the world of matrices further.

​They had learnt that matrices were arrays of numbers and determinants were special numbers associated with these matrices.They started with finding the determinant of a 2 by 2 matrix. Moving on to a 3 by 3 matrix, they decided to expand it by the first row, in order to find the determinant.

Sarah and John went on further to calculate determinants of larger matrices. Their passion for the subject grew and they realised that with perseverance and hard work they could solve any problem they set their mind to. The two friends graduated from high school and carried their liking for mathematics in their respective careers.

I am Suman Mathews, online Math tutor and educator. I can tell you how exactly you should be learning Determinants for Class 12 Mathematics CBSE and ISC.. Reading this post, beforehand will ensure that you don't miss out on any topic before the exams.

Determinants and Matrices is one of the easiest topics in Class 12. Almost all of my students get this topic right. Just ensure that you have a knowledge of Matrices before you start learning Determinants.

## What is a Determinant of a Matrix?

To start with, a determinant is a number attached to a square matrix. You will learn how to expand a determinant by any row or column. If A is a square matrix and k is any scalar, what is determinant of kA.

You can access all the formulas in the youtube link provided here.

You can use determinants to find the area of a triangle. This is an important concept. Note that, if the area of the triangle is zero, the points are collinear.

## Minors and Cofactors

Minor of any element in a determinant of order n is a determinant of order n-1. Access the formula for minors and cofactors in this video. Once you learn how to calculate the cofactors of a matrix, you can progress to calculating the adjoint of a matrix.

Access more properties of adjoint of a matrix in the video link. A square matrix is said to be singular, if its determinant is equal to zero. And again, if a matrix is non singular its, inverse exists.

There are umpteen problems on this concept. Again, note that this is an important topic which carries considerable weightage in your exams.

## Do you need extra help?

Though this topic of Determinants is incredibly easy, you may still need some extra help in studying this. Feel free to register for my webinar on Determinants. The entire topic may require 4 to 5 classes of one hour each.

I will be teaching MCQ based questions, questions based on logical reasoning and case study based questions as well together with long answer questions. These are in tune with the NEP model as framed by ISC, NCERT. For further queries, you can contact me on mathews.suman@gmail.com

I hope this was useful to you. You can access the formulas given in the links. Would you like to help other students who need that little extra help in Mathematics.

If so, kindly share this with your friends and relatives.All my students have scored well in their exams.You can also visit my website www.sumanmathews.com for more free resources.

Until we meet again!