WHY SOME STUDENTS ALWAYS DO WELL IN MATHEMATICS!
If you are studying Mathematics in Class 12, Matrices and Determinants may seem to be a pretty easy topic for you.
But yet, there are certain topics such as finding the inverse of a matrix using elementary operations and properties of Determinants using elementary operations which are a little tricky.
I encourage you to join hands with me, an experienced math teacher to cross the threshold to understanding this topic better.
This page has a number of free resources and videos which will prove useful to you. Feel free to dive into any of these any time.Finally, an important tip is that you nee to practice mathematics everyday for at least an hour.
This will help you overcome your exams with ease and reap the harvest of success.
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Learn how to multiply 2 matrices. 2 matrices A and B can be multiplied if the number of columns of the 1st matrix = number of rows of the 2nd matrix. Matrix multiplication is not commutative and also learn what is a matrix polynomial. 2 problems on matrix multiplication are illustrated.
PROBLEMS ON MATRIX MULTIPLICATION AND PROPERTIES OF TRANSPOSE OF A MATRIX
Learn an interesting application problem on matrix multiplication. Also, get introduced to transpose of a matrix and its properties.
SYMMETRIC AND SKEW SYMMETRIC MATRICES
What are symmetric and skew symmetric matrices? You will see the properties of symmetric and skew symmetric matrices and how any square matrix can be written as the sum of a symmetric and skew symmetric matrix
HOW TO FIND THE INVERSE OF A MATRIX USING ELEMENTARY ROW/COLUMN OPERATIONS
A slightly difficult topic where we learn how to use elementary row or column operations to find the inverse of a matrix. We need to remember that when elementary row operations are used, we pre multiply by the identity matrix and first try to make the lower triangle zero. When elementary column operations are used, we post multiply by the identity matrix and focus on making the upper triangle zero. Time and again, I have repeated this concept with my students as each problem in different. I have made a video explaining this.
MINORS AND COFACTORS
We move to Determinants. You are introduced to minors and cofactors . You will notice the subtle difference between a minor and cofactor. These are likely to be asked as objective questions.
EXPANSION OF A DETERMINANT AND PROPERTIES OF ADJOINT
Using properties of minors and cofactors, learn how a determinant can be expanded by any row or column. Also , study the properties of adjoint of a matrix and inverse of a matrix.
PROBLEMS ON ADJOINT PROPERTIES AND HOW TO CALCULATE THE ADJOINT
Very important properties of Adjoint of a matrix are shown here. How do you calculate A( ADJOINT A) without calculating the Adjoint. Also, learn how to evaluate Adjoint of a 3 by 3 matrix.
HOW TO SOLVE A SYSTEM OF EQUATIONS USING MATRICES AND DETERMINANTS
I am showing you a simple way to solve a system of equations. This is called Martin's rule. You will first write the system of equations in the matrix form and then check if the determinant of the coefficient matrix is not zero. If it is not zero, we use a simple formula to calculate the inverse.
PROPERTIES OF DETERMINANTS
Learn how to apply properties of Determinants in solving problems. While trying to solve these problems using properties of Determinants, it is useful to remember that each problem is different. There is no one sure method to do any problem . You can use any property and then work towards the answer if you apply the properties correctly. Online classes are also provided , in case you are interested. You can opt for a specific topic or the entire course. For more details, you can contact me on email@example.com
HOW TO SOLVE A SYSTEM OF EQUATIONS USING MATRICES/DETERMINANTS
How do you solve a system of 3 equations in 3 unknowns? How do you find the inverse of a matrix? Learn this and much more by watching this video. Here, we learn how to calculate the inverse of a 2 by 2 and 3 by 3 matrix. We learn about adjoint of a matrix and how it is used to solve a system of equation. We consider the cases of a unique solution, infinitely many solutions or inconsistency of the equations.
VIDEO ON MCQ'S IN DETERMINANTS