This is the question. The following is the solutions I found:
I understand that the first line was derived by setting one vertex on origin and taking the transpose of the matrix. However, I cannot understand where the extra row and column came from in the second line. Can anyone explain how...
question:
My first attempt:
my second attempt:
So I am getting 0 (the right answer) for the first method and 40 for the second method. According to the theorem, shouldn't the determinant of the matrix remain the same when the multiple of one row is added to another row? Can anyone explain...
Hi all, I'm doing undergraduate research this summer, and a few times I've been told to calculate a term with the following form: ∈abcdpaqbkcsd, where p,q,k and s are four vectors (four-momentum, spin, etc). Now I know this ends up calculating exactly like a 4x4 determinant, I'm just not quite...
Homework Statement
Refer given image.
Homework Equations
Expansion of determinant.
w^2+w+1=0 where w is cube root of 1.
The Attempt at a Solution
Expanding the determinant I got cw^2+bw+a-c=0. Well after that I have no idea how to proceed.
Homework Statement
Show that for a second order cartesian tensor A, assumed invertible and dependent on t, the following holds:
## \frac{d}{dt} det(A) = det(a) Tr(A^{-1}\frac{dA}{dt}) ##
Homework Equations
## det(a) = \frac{1}{6} \epsilon_{ijk} \epsilon_{lmn} A_{il}A_{jm}A_{kn} ##
The...
Hi.
I'm reading an article about QCD phase diagram. https://arxiv.org/abs/1005.4814.
I want to derive eq(20), but I don't know how.
Does anyone know how to derive this?
Homework Statement
Let A,B,C,D be commuting n-square matrices. Consider the 2n-square block matrix ##M= \begin{bmatrix}
A & B \\
C & D \\
\end{bmatrix}##. Prove that ##\left | M \right |=\left | A \right |\left | D \right |-\left | B \right |\left | C \right |##. Show that the result may not be...
Basically I don't know how to get to the constraints from the system of equations. In class we used det to find constraints for homogenous equations, but we didn't go over this situation. Someone spell it out for me?
Homework Statement
Homework Equations
determinant is the product of the eigenvalues... so -1.1*2.3 = -2.53
det(a−1) = 1 / det(A), = (1/-2.53) =-.3952
The Attempt at a Solution
If it's asking for a quality of its inverse, it must be invertible. I did what I showed above, but my answer was...
Homework Statement
Show that the determinant of
is (a-b)(b-c)(c-a)
Homework Equations
Row reduction, determinants
The Attempt at a Solution
Apparently I got a (a-b)^2 instead of (a-b) when I multiplied them up. It would be grateful if someone can point me out where the mistakes are.
I have a problem of proving an identity about determinants. For ##A\in M_{m\times n}(\mathbb{R}),## a matrix with ##m## rows and ##n## columns, prove the following identity.
$$|\det(A^tA)|=\sum_{1\le j_1\le ... \le j_n \le m} (det(A_{j_1...j_n}))^2$$
where ##A_{j_1...j_n}## is the matrix whose...
Hello I was learning about determinants and matrices. I learned the generalization of getting the determinant of an n by n matrix. I then applied this to vector space (i + j + k) via a cross product and noticed that you leave the i j and k in their own columns in the first row of the matrix...
The determinant of a 3x3 matrix can be interpreted as the volume of a parallellepiped made up by the column vectors (well, could also be the row vectors but here I am using the columns), which is also the scalar triple product.
I want to show that:
##det A \overset{!}{=} a_1 \cdot (a_2 \times...
Homework Statement
I'm a bit at a loss - I thought the last row with '1's would be useful, but it just gave me:
(b2c - bc2) - (a2c - ac2) + (a2b - ab2)
and
bc(b - c) - ac(a - c) + ab(a - b)
But then it is a dead end. I am probably doing something stupid again ...
Any help appreciated.
Homework Statement
A determinant a is defined in the following manner ar * Ak = Σns=1 ars Aks = δkr a , where a=det(aij), ar , Ak , are rows of the coefficient matrix and cofactor matrix respectively. The second term in the equation is the expansion over the columns of both matrices, δkr is...
I just did this following exercise in my text
If C is the line segment connecting the point (x_1,y_1) to (x_2,y_2), show that
\int_C xdy - ydx = x_1y_2 - x_2y_1
I did, and I also noticed that if we put those points into a matrix with the first column (x_1,y_1) and the second column (x_2,y_2)...
Hi,
How would you solve a singular matrix? ie when determinant is zero.
Lets assume an equation, (1) Ax+By=E and (2) Cx+Dy=F
if the determinant; AD-BC = 0, and therefore the matrix is singular, How to go around solving the equation?
LU decomposition, Gaussian elimination?
Ideally I am...
Can anyone explain or point me to a good resource to understand these operators? I'm trying to the understand determinants for skew symmetric matrices, more specifically the Moore determinant and it's polarization of mixed determinants. Can hone shed some light? I'm confused as to how the...