Question

If the value of third order determinant is 11. Then what is the value of the determinant formed by its cofactors.

Answer 1

Answer:

146.41

Step-by-step explanation:

third order determinant = determinant of 3×3 matrix A

given ∣A∣=11

det (cofactor matrix of A) =set (transpare of cofactor amtrix of A) (transpare does not change the det)

=det(adjacent of A)

{det (cofactor matrix of A)}  ^2  = {det (adjacent of A)} ^2

 

(Using for an n×n det (cofactor matrix of A)=det (A)^n−1 )

we get

det (cofactor matrix of A)^2  = {det(A)  ^3−1 }^2

 

=(11)^2×2  = 11^4

 =146.41