Question

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

(Please show Solution)
CBSE Grade 12

Answer 1

146.41

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