Obtaining the Inverse of a 3 x 3 Matrix

Having obtained the determinant of a 3 x 3 matrix, it is quite straightforward to obtain its inverse matrix. Below we will present the steps that one follows to obtain the inverse of a matrix of order 3 and illustrate the method bv means of an example.

Step 1 Corresponding to the elements (/ยก, of A, we obtain the cofactors C1(, /' = 1.2, 3; j = 1,2, 3. Then we form a matrix in which each element a,, is replaced by the corresponding cofactors C,,, given below as

CM C12 C|j C21 C22 C23 C.hi C32 C33

9 2 OBTAINING THE DETERMINANT AND INVERSE OF A 3x3MATRIX 373

Step 3 Transpose the matrix obtained in the first step. The resulting matrix is known as the adjoint matrix of the original matrix -4. The adjoint matrix is denoted by adj(A) and is given by adj(/4) =

Step 4 Once we have obtained adj(/t). we divide each of its elements by |/t|. The resulting matrix is A-1. This is given by

|A|

Cu

0 0

Post a comment