Understanding Matrices and Determinants-Mathematics-Class 12
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.
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.