Problem involving the adjugate

  • Thread starter Thread starter wakko101
  • Start date Start date
wakko101
Messages
61
Reaction score
0
The question I'm dealing with is this:

Suppose adj(A) =
-1 2 -4
0 -3 0
0 0 3
Find A

I was trying to figure it out backwards, by using a 3x3 matrix of variables and doing the cofactor expansion thing and then seeing if I could figure out the values of the variables, but I'm not sure that's the way to go. I suspect there is a formula or theorem out there that will help me, but I can't figure out what it is.

Any help?
 
Physics news on Phys.org
Is the determinant of A given?
If it is so you can use A*adj(A)=det(A) *identity matrix
But if it is not i don't know what to do
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
Back
Top