Question

Determinant with ones on diagonal and increasing powers of a constant in rows and columns

score 182 · Answer 1 · 2026-03-31 14:54:07

182

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Determinant with ones on diagonal and increasing powers of a constant in rows and columns

Published on 31 Mar 2026 - 14:54

score 392 · Answer 2 · 2019-11-30 02:03:52

392

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Show that following determinant is divisible by $\lambda^2$ and find the other factor.

Published on 30 Nov 2019 - 2:03

score 149 · Answer 3 · 2019-11-30 10:53:33

Prove $\left|\begin{smallmatrix}a&b-c&c+b\\a+c&b&c-a\\a-b&b+a&c\end{smallmatrix}\right|=(a+b+c)(a^2+b^2+c^2)$ without direct evaluation

score 70 · Answer 4 · 2019-11-30 13:52:48

70

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If $p+q+r=0$, prove these determinants are equal

Published on 30 Nov 2019 - 13:52

score 118 · Answer 5 · 2019-11-30 23:02:33

118

Views

Show that the determinant $\mathcal{D}(\mathbf{x}, \mathbf{y})$ is the signed area of the parallelogram spanned by $\mathbf{x}$ and $\mathbf{y}$.

Published on 30 Nov 2019 - 23:02

score 69 · Answer 6 · 2019-12-02 01:34:03

69

Views

Finding a solution for a simple conjecture

Published on 02 Dec 2019 - 1:34

score 110 · Answer 7 · 2019-12-02 15:09:21

110

Views

Determinant of a 3*3 matrix of cosines

Published on 02 Dec 2019 - 15:09

score 136 · Answer 8 · 2026-03-30 01:14:51

136

Views

What's the probability a 3x3 circulant matrix with natural coefficients < n is nonsignular?

Published on 30 Mar 2026 - 1:14

score 67 · Answer 9 · 2019-12-02 23:59:00

67

Views

Is it necessary $A^TA =I$ if $AA^T=I$ where A is a square matrix?

Published on 02 Dec 2019 - 23:59

score 31 · Answer 10 · 2026-03-27 00:59:13

31

Views

Multplying $n \times (n-1)$ matrix $B$ by orthogonal $V$ and augmenting basis vector, yields same determinant as augmenting matrix by element of $V$

Published on 27 Mar 2026 - 0:59

score 242 · Answer 11 · 2019-12-03 10:02:26

242

Views

Interchange of rows changes the sign of the determinant

Published on 03 Dec 2019 - 10:02

score 74 · Answer 12 · 2026-03-27 04:15:00

74

Views

Semplification using Vandermonde determinant

Published on 27 Mar 2026 - 4:15

score 133 · Answer 13 · 2019-12-03 13:57:52

133

Views

Almost a Vandermonde matrix

Published on 03 Dec 2019 - 13:57

score 196 · Answer 14 · 2026-03-28 14:00:33

196

Views

True/false: $\det(A^2+I)\ge 0$ for every $3 \times 3$ matrix with real entries and rank $>0$

Published on 28 Mar 2026 - 14:00

score 904 · Answer 15 · 2019-12-04 12:13:02

904

Views

If $AX = U$ has infinitely many solutions, then prove that $BX=V$ cannot have a unique solution.

Published on 04 Dec 2019 - 12:13

List Question

Determinant with ones on diagonal and increasing powers of a constant in rows and columns

Show that following determinant is divisible by $\lambda^2$ and find the other factor.

Prove $\left|\begin{smallmatrix}a&b-c&c+b\\a+c&b&c-a\\a-b&b+a&c\end{smallmatrix}\right|=(a+b+c)(a^2+b^2+c^2)$ without direct evaluation

If $p+q+r=0$, prove these determinants are equal

Show that the determinant $\mathcal{D}(\mathbf{x}, \mathbf{y})$ is the signed area of the parallelogram spanned by $\mathbf{x}$ and $\mathbf{y}$.

Finding a solution for a simple conjecture

Determinant of a 3*3 matrix of cosines

What's the probability a 3x3 circulant matrix with natural coefficients < n is nonsignular?

Is it necessary $A^TA =I$ if $AA^T=I$ where A is a square matrix?

Multplying $n \times (n-1)$ matrix $B$ by orthogonal $V$ and augmenting basis vector, yields same determinant as augmenting matrix by element of $V$

Interchange of rows changes the sign of the determinant

Semplification using Vandermonde determinant

Almost a Vandermonde matrix

True/false: $\det(A^2+I)\ge 0$ for every $3 \times 3$ matrix with real entries and rank $>0$

If $AX = U$ has infinitely many solutions, then prove that $BX=V$ cannot have a unique solution.

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