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Matrices: Minors and Cofactors Video Lecture | Mathematics for Competitive Exams

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FAQs on Matrices: Minors and Cofactors Video Lecture - Mathematics for Competitive Exams

1. What are minors and cofactors in matrices?
Ans. In matrices, a minor refers to the determinant of a smaller matrix obtained by removing one or more rows and columns from the original matrix. On the other hand, a cofactor is the signed minor, where the sign is determined by the position of the element in the original matrix.
2. How are minors and cofactors used to find the inverse of a matrix?
Ans. To find the inverse of a matrix, the minors and cofactors play a crucial role. The adjugate of a matrix is obtained by replacing each element with its corresponding cofactor. Then, the inverse of the matrix is found by dividing the adjugate by the determinant of the original matrix.
3. What is the significance of minors and cofactors in solving systems of linear equations using matrices?
Ans. Minors and cofactors are used to calculate the determinant of a matrix. The determinant helps determine if a system of linear equations has a unique solution, no solution, or infinitely many solutions. By evaluating the minors and cofactors, we can determine the determinant and thus analyze the system of equations.
4. Can minors and cofactors be used to find the rank of a matrix?
Ans. Yes, minors and cofactors can be used to find the rank of a matrix. The rank of a matrix is equal to the maximum number of linearly independent rows or columns it contains. By examining the size and properties of the minors and cofactors, we can determine the rank of the matrix.
5. Are minors and cofactors only applicable to square matrices?
Ans. Yes, minors and cofactors are primarily used for square matrices. Square matrices have an equal number of rows and columns, allowing the determination of minors and cofactors. However, certain concepts related to minors and cofactors can be extended to rectangular matrices as well.
98 videos|27 docs|30 tests

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