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Minors and Cofactors : Example Video Lecture | Mathematics (Maths) Class 12 - JEE
FAQs on Minors and Cofactors : Example Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. What is a minor of a matrix? |  |
Ans. A minor of a matrix is the determinant of a square submatrix obtained by deleting some rows and columns from the original matrix. It provides information about the linear dependence or independence of the rows or columns of the matrix.
| 2. How do you calculate the minor of a matrix? | |
Ans. To calculate the minor of a matrix, choose a square submatrix by deleting some rows and columns. Then, take the determinant of the submatrix. This determinant is the minor of the matrix.
| 3. What is a cofactor of a matrix? | |
Ans. A cofactor of a matrix is the signed minor obtained by multiplying a minor with a sign factor determined by the position of the element in the matrix. The sign factor alternates between positive and negative for each element.
| 4. How do you calculate the cofactor of a matrix? | |
Ans. To calculate the cofactor of a matrix, first calculate the minor of the matrix. Then, multiply the minor by a sign factor determined by the position of the element. The sign factor is positive if the sum of the row number and column number is even, and negative if it is odd.
| 5. What is the relationship between minors and cofactors? | |
Ans. The relationship between minors and cofactors is that each cofactor is obtained by multiplying the corresponding minor with a sign factor. The sign factor determines the position of the element in the matrix and alternates between positive and negative. The cofactors are used in the calculation of the adjugate and the inverse of a matrix.
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