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.
VIDEO ON MCQ'S IN DETERMINANTS