Question

determinant of linear map
link: http://puu.sh/cJBk2/581a41f86e.png

Answer 1

@asnaseer @dumbcow

Answer 2

is it just find a matrix that when the 1st matrix multiplies with that, it gives the 2nd matrix

Answer 3

yeah so

\[f = \left[\begin{matrix}a &b \\ c & d\end{matrix}\right]^{-1} (..)\]

Answer 4

the 2nd part matrix is in parenthesis

Answer 5

ok this is how i see it, let 1st matrix=A, 2nd matrix=B, the matrix we want to find=C
AB=C
B=A^-1*C
det(B)=det(C)det(A)^-1

Answer 6

am i right?

Answer 7

change B and C around
we want to find matrix B

Answer 8

why we want to multiply the A(the input matrix) with C(the output matrix)? :c

Answer 9

WAIT MY BAD LOL I CHOKED WHEN I WROTE U ARE RIGHT

Answer 10

a friend of mine suggested another solution, he said something like first choose a basis, then find the target in terms of basis, write that as f_basis, then find det()
is he making any sense? :x

Answer 11

possibly it sounds good, sorry im not very good when it comes to change of basis

Answer 12

your equation will work though

det(f) = det(C) * 1/det(A)

Answer 13

kk man thanks a lot!