#What did they make to the matrix here?
wraith narwhalBOT
- Wait patiently for a helper to come along.
- Once someone helps you, say thank you and close the thread with:
+close
- Feel free to nominate the person for helper of the week in #helper-nominations
- Do not ping the mods, unless someone is breaking the rules.
- If you're happy with the help you got here, and the server overall, you can contribute financially as well:
spice osprey
look up Cramer's Rule
carmine radish
yeah tbh now i regret not saying i understand what they did
which is a cofator matrix
but i dont know how they did it so fast
spice osprey
Well do you know what a cofactor is?
carmine radish
i do
spice osprey
the cofactor matrix is the matrix of cofactors
ie $C=[C_{ij}]$, where $C_{ij}$ is the $(i,j)$ cofactor
merry geodeBOT
Omegabet_
carmine radish
yeah but making one doesnt mean going through all those calculations for each element
im not against hard work
its just that its odd, considering this is for a multiple choice question
heres the question albeit in pt
spice osprey
well the question looks like it's to find a solution/part of a solution to some Ax=b
carmine radish
they want me to find the element of the inverse matrix in A23
spice osprey
so then yeah, you're just computing 1 cofactor
carmine radish
Oh really?
spice osprey
yeah
carmine radish
uh then i divide that value by the det value?
spice osprey
$A^{-1}=\frac{1}{\det(A)}\text{adj}(A)$, where the adjugate is the transpose of the cofactor matrix
merry geodeBOT
Omegabet_
carmine radish
that makes a lot of sense then, and plus, to solve the cofactor of this element in a order 4 matrix
do i just do it like the LaPlace Theorem?
add up the values that is
spice osprey
Laplace expansion computes determinants, so yes you'll need that or some other formula for the determinant
carmine radish
oh alright
ill try doing this, if it goes right ill thank you here and close this then
spice osprey
but like, computing det(A) is trivial since A is (upper) triangular
so the only possibly hard part is finding the correct cofactor
carmine radish
apparently it really does look easy but i aint figuring it out
i did try to do the cofactor of the said value and divide by the inverse
but it gives me 0
wait
spice osprey
$C_{3,2}=(-1)^{3+2}\begin{vmatrix}1&1&-1\0&2&2\0&0&2\end{vmatrix}$
something like that
merry geodeBOT
Omegabet_
spice osprey
cause you remove the 3rd row and 2nd column, then compute that minor's determinant
carmine radish
my problem is that this solution is going in a whole different direction
they have a whole different matrix on the cramer equation
we re probably doing this wrong
WAIT
oh my god, im so sorry man
i was looking at the wrong solution
spice osprey
sounds about right lol
cause yeah, that solution is very much for something related to Cramer's
carmine radish
ill try doing this again then
Still aint right
supposedly the answer is -1
maybe since we re lookin for the value in the inverted matrix we first adjoint the cofator matrix?
as in , look for A 32 instead of A 23
spice osprey
well yeah
like I said, adj(A) is the transpose of the cofactor matrix
so the (2,3) entry is C_(32)/|A|
carmine radish
yup that did it
so basically to make sure i got that right
i got the cofator matrix for 2,3
adjointed it
and then went for 3,2 instead
thats how you get that right
carmine radish
the right answer is -1 though
and since the determination is 4 since its a triangular matrix and you just multiply the elements of the diagonal
carmine radish
wait sorry, but how do you solve the cofator
as in, that cofator with the 3 entries
the only way i solved it was to do the laplace theorem in C32
spice osprey
wait sorry, but how do you solve the cofator
just compute it
$C_{ij}:=(-1)^{i+j}\det(\hat{A}{ij})$, where as usual $\hat{A}{ij}$ is the minor gotten from deleting the $i$th row and $j$th column
merry geodeBOT
Omegabet_
