Question

Determinant of $\left(\begin{smallmatrix} -bc & b^2+bc & c^2+bc \\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{smallmatrix}\right)$

score 67 · Answer 1 · 2019-07-19 14:59:46

Determinant of $\left(\begin{smallmatrix} -bc & b^2+bc & c^2+bc \\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{smallmatrix}\right)$

score 31 · Answer 2 · 2026-03-27 14:45:18

31

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score 52 · Answer 14 · 2019-08-01 12:58:25

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score 72 · Answer 15 · 2026-03-26 03:13:37

72

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List Question

Determinant of $\left(\begin{smallmatrix} -bc & b^2+bc & c^2+bc \\ a^2+ac & -ac & c^2+ac \\ a^2+ab & b^2+ab & -ab \end{smallmatrix}\right)$

Can you help me with the 4th option?

A problem about Vandemonde matrix

Application of Rolle's theorem and determinant

Vandermonde determinant of the elements of a finite field

How to derive this matrix formula with "vector inversion" which sometimes works and sometimes doesn't?

How to show the following problem regarding determinant

Determinant of a diagonal block matrix using exterior algebra

What is the value of this determinant? [2]

Resultant of homogeneous polynomials and composition

Simplifying the determinant of the matrix whose $(i,j)$-th entry is $b_i c_j$ for $i=j$ and $-b_i c_j$ for $i\neq j$

Convexity of a log-determinant function

Why does $A^{-1} = \frac{1}{|A|} \cdot \operatorname{adj}(A)$ work, intuitively?

How can I prove that for a matrix $B$ with elements $b_{ij} = k^{i-j} a_{ij}$ this is true: $\det(B) = \det(A)$

Let, there be a matrix of order $N$ with all distinct entries. Using the given entries, is the sum of determinants of all possible matrices zero?

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