The adjoint determinant is the (n - I) th power of the original determinant.
The adjoint determinant will be seen subsequently to present itself in the theory of linear equations and in the theory of linear transformation.
It is easy to see that the adjoint determinant is also 'symmetrical, viz.
For the second order we may take Ob - I - A, 1 1 +A2, and the adjoint determinant is the same; hence (1 +A2)x1 = (1-A 2)X 1 + 2AX2, (l +A 2)x 2 = - 2AX1 +(1 - A2)X2.
In 1768, recognized as a man who had both the ability and the means for a scientific career, he was nominated adjoint chimiste to the Academy, and in that capacity made numerous reports on the most diverse subjects, from the theory of colours to water-supply and from invalid chairs to mesmerism and the divining rod.