Matrices and Determinants for Class 12: Key Concepts and Shortcuts

Matrices and Determinants for Class 12 Math

Matrices and Determinants is an integral part of Class 12 Mathematics. I am Suman Mathews, math teacher teaching mathematics for the past three decades. I hope this helps you to learn matrices and Determinants for Class 12 Math in the right way and score better in this topic.

This blog gives you a gist of all the topics that you need to cover for your exams. It starts from the basics and moves upwards. You are encourages to click on the links provided which gives you a lot of free lessons tailored for your exams.

I am a math educator and content developer with a teaching experience of three decades. Having taught math at the college and high school level, I can adapt my teaching to suit your individual style. I believe in Math Made Easy, making math concepts easy for you.

So what is a matrix?

A matrix is a rectangular arrangement of rows and columns. The horizontal entries are called rows and the vertical entries are called columns. A matrix having only one row is called a row matrix and a matrix having only one column is called a column matrix. In a null matrix, every element is zero. A matrix having the same number of rows and columns is called a square matrix.

What about diagonal matrices?

A diagonal matrix is a matrix where all non diagonal elements are zero. Scalar matrix is a matrix whose diagonal elements are zero. Identity matrix is a scalar matrix whose diagonal elements are unity. There's also an upper triangular and lower triangular matrix. Next, you'll need to know about matrix addition and scalar multiplication.

How is matrix multiplication used?

Moving on to matrix multiplication, two matrices A and B can be multiplied if the number of columns of the first matrix is equal to the number of rows of the second. Matrix multiplication is not commutative but it is associative.

Transpose of a matrix is obtained by interchanging the rows and columns. A square matrix is said to be symmetric if A transpose is equal to A. It is skew symmetric if A transpose is equal to -A.

How about symmetric and skew symmetric matrices?

Every matrix can be written as the sum of a symmetric and skew symmetric matrix. Moving on to determinants. For a square matrix A, we can associate a number which is called the determinant of A, denoted by det A. In class twelve, we mainly focus on finding the determinant of a 2 by 2 and 3 by 3 matrix. The determinant obtained from a square matrix by deleting the ith row and the j th ccolumn is called the minor of the matrix. We also learn about cofactor of a matrix.

Let's expand determinants!

Note that a determinant can be expanded by any row or column. Determinant of a skew symmetric matrix of odd order is zero. If A and B are two square matrices of the same order, det(AB)= det(A) det(B). You now learn about adjoint of a matrix which is the transpose of the cofactor matrix. You also learn to calculate the inverse of a matrix using it's adjoint.

Coming to inverse of a matrix-

Note that inverse of a matrix is unique. A square matrix is said to be singular if it's determinant is equal to zero. If it's determinant is not equal to zero, it is non singular. If a matrix is non singular, it's inverse exists. There are a number of properties of adjoint which we will learn. You can contact me for online tutoring if you need help.

Solving Matrix Equations-

Matrix equations can be solved using Cramer's Rule and Adjoint of a matrix. In Cramer's Rule. you solve a system of equations. In Class Twelve, you'll mostly focus on two or three unknown variables. Youll also learn the matrix method or Martin's method to solve a system of equations. This makes use of the adjoint of a matrix.

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