Theorems related to Adjoint of a Matrix and Inverse of Matrix

# Theorems related to Adjoint of a Matrix and Inverse of Matrix Video Lecture | Mathematics (Maths) Class 12 - JEE

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

## FAQs on Theorems related to Adjoint of a Matrix and Inverse of Matrix Video Lecture - Mathematics (Maths) Class 12 - JEE

 1. What is the adjoint of a matrix?
Ans. The adjoint of a matrix is the transpose of its cofactor matrix. It is also known as the adjugate matrix. The adjoint of a matrix A is denoted as adj(A).
 2. How can the adjoint of a matrix be used to find the inverse of the matrix?
Ans. The adjoint of a matrix can be used to find the inverse of the matrix by dividing the adjoint of the matrix by the determinant of the matrix. The formula to find the inverse of a matrix A is A^(-1) = adj(A) / det(A).
 3. What is the relationship between the adjoint and inverse of a matrix?
Ans. The inverse of a matrix can be obtained by taking the adjoint of the matrix and dividing it by the determinant of the matrix. In other words, the inverse of a matrix A is equal to the adjoint of A divided by the determinant of A.
 4. Can a matrix have an inverse if its adjoint does not exist?
Ans. No, a matrix cannot have an inverse if its adjoint does not exist. The adjoint of a matrix is necessary to calculate its inverse. If the adjoint does not exist, it means that the matrix does not satisfy the necessary conditions for an inverse to exist.
 5. How can the adjoint of a matrix be calculated?
Ans. To calculate the adjoint of a matrix, we need to find the cofactor matrix of the given matrix and then take its transpose. The cofactor matrix is obtained by multiplying each element of the matrix by its corresponding cofactor, which is the determinant of the submatrix formed by excluding the row and column of the element. Once we have the cofactor matrix, we can take its transpose to get the adjoint of the matrix.

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

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