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What are Minors and Cofactors? Video Lecture | Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

Timeline

00:03 Determinant of a Matrix Formula
01:43 What is a Minor?
01:55 What is a Cofactor?
02:30 How to find Minor & Cofactors?
03:15 Relation between Minor & Cofactor
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FAQs on What are Minors and Cofactors? Video Lecture - Mathematics (Maths) for JEE Main & Advanced

1. What are minors and cofactors in linear algebra?
Ans. In linear algebra, minors and cofactors are terms used to describe the determinants of submatrices within a larger matrix. A minor is the determinant of a square submatrix obtained by deleting certain rows and columns from the original matrix, while a cofactor is the signed minor, where the sign depends on the position of the submatrix within the original matrix.
2. How are minors and cofactors used in finding the inverse of a matrix?
Ans. Minors and cofactors play a crucial role in finding the inverse of a matrix. By computing the minors and cofactors of each element in the matrix, you can construct the adjugate matrix. The inverse of the original matrix is then obtained by dividing the adjugate matrix by the determinant of the original matrix.
3. What is the significance of minors and cofactors in solving systems of linear equations?
Ans. Minors and cofactors are important in solving systems of linear equations because they help in finding the determinant of a matrix. The determinant provides information about the solvability of the system and the number of solutions it has. By using minors and cofactors, you can determine if a system of linear equations has a unique solution, no solution, or infinitely many solutions.
4. Can minors and cofactors be used to solve eigenvalue problems?
Ans. Yes, minors and cofactors can be used to solve eigenvalue problems. In the process of finding eigenvalues and eigenvectors, you need to compute the characteristic polynomial of a matrix. The coefficients of this polynomial can be determined using minors and cofactors. By solving the characteristic polynomial, you can find the eigenvalues of the matrix.
5. Are minors and cofactors applicable only to square matrices?
Ans. Yes, minors and cofactors are applicable only to square matrices. Since minors and cofactors involve computing determinants, which are defined only for square matrices, they are not relevant for non-square matrices. However, they are widely used in various applications involving square matrices, such as solving systems of linear equations, finding the inverse of a matrix, and solving eigenvalue problems.
209 videos|443 docs|143 tests

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