explain inverse of the matrix
Answers
Answer:
Step-by-step explanation
-1 = A-1A = I, where I is the identity matrix.
The inverse of a 2×2 matrix
Take for example an arbitrary 2×2 Matrix A whose determinant (ad − bc) is not equal to zero.
where a, b, c and d are numbers.
The inverse is:
The inverse of a general n × n matrix A can be found by using the following equation.
where the adj (A) denotes the adjoint of a matrix. It can be calculated by the following method:
Given the n × n matrix A, define B = bij to be the matrix whose coefficients are found by taking the determinant of the (n-1) × (n-1) matrix obtained by deleting the ith row and jth column of A.
The terms of B (i.e. B = bij) are known as the cofactors of A.
Define the matrix C, where cij = (−1)i+j bij.
The transpose of C (i.e. CT) is called the adjoint of matrix A.