Q. 65.0( 3 Votes )

Find the inverse

Answer :

Let the given matrix we have to find A-1.


Now A-1 will exist only of |A| ≠ 0


Let us first find |A|



|A| = (-3) (-3) – (5)(2)


|A| = 9 – 10 = -1


Hence |A| ≠ 0 and A-1 exist


Now A-1 is given by



Now adjoint(A) = CT where C is the cofactor matrix and CT is the transpose of cofactor matrix


The cofactor is given by


Cij = (-1) i+jMij …(a)


Where M represents minor


Mij is the determinant of matrix leaving the ith row and jth column


The cofactor matrix C will be



Now transpose of C that is CT


For CT we will interchange the rows and columns



Using (a)



From matrix A the minors are


M11 = -3, M12 = 5, M21 = 2 and M22 = -3




Now inverse of A is





Now we have to solve the matrix equation




As we know that AA-1 = I hence multiply equation by A-1 from right side where I is identity matrix






Hence


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