1) How do you find A (by hand) if an adjoint of A 4 by 4 matrix is given you?
Adj A equals
2 0 0 0
0 2 1 0
0 4 3 2
0 -2 -1 2
what is A?
I know that A (adj. A) = (det. A) I
and I tried to find A by finding the Adj. A of the given Adj. of A and I got the weird numbers.
The answer is suposed to give the following matrix:
1 0 0 0
0 4 -1 1
0 -6 2 -2
0 1 0 1
How do you get to that? I had asked this several days ago and the links I received sort of helped but I got confused again. I tried to solve this twice and its frustrating that I am not getting the answer. Please if anyone could explain this with baby steps I don't mind at all I just want is to understand it. Thanks
2) Let R denote the set of real numbers. Define scalar multiplication by
a x= a *x (the usual multiplication of real numbers)
and define the addition, denoted Å , by
x Å y = max (x, y) (the maximum of the two numbers)
Is R a vector space with these operations? Prove your answer.
( I have no idea how to solve this one either)