Question

Proving the determinant of this matrix is $0$: $\left(\begin{smallmatrix}2&1&0&5\\-1&1&1&6\\5&1&-1&4\\5&1&3&0\end{smallmatrix}\right)$

score 166 · Answer 1 · 2018-05-12 20:28:23

166

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Proving the determinant of this matrix is $0$: $\left(\begin{smallmatrix}2&1&0&5\\-1&1&1&6\\5&1&-1&4\\5&1&3&0\end{smallmatrix}\right)$

Published on 12 May 2018 - 20:28

score 1k · Answer 2 · 2026-03-26 14:23:07

1k

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Prove that the set of $n \times n$ matrices with determinant $1$ is unbounded closed with empty interior in $\mathbb{R}^{n^{2}}$.

Published on 26 Mar 2026 - 14:23

score 9.8k · Answer 3 · 2026-03-25 17:40:34

9.8k

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If $\lambda$ is an eigen value of an orthogonal matrix $A$, then show that $\frac{1}{\lambda}$ is also an eigen value of $A$

Published on 25 Mar 2026 - 17:40

score 41 · Answer 4 · 2018-05-13 08:18:09

Prove: Let $ A\in\mathsf{Mat}(2\times 2, \mathbb{R})$. If $ \det(A)$ is zero, then there exist a $ \mu\in\mathbb{R}$, so that $ \mu A = A^2$.

score 54 · Answer 5 · 2018-05-13 12:43:23

54

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Determinant and solution of equations

Published on 13 May 2018 - 12:43

score 638 · Answer 6 · 2026-03-26 01:34:58

638

Views

Change negative area of triangle into positive area!

Published on 26 Mar 2026 - 1:34

score 1.1k · Answer 7 · 2018-05-14 19:25:49

1.1k

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Calculate the determinant of this $5 \times 5$ matrix

Published on 14 May 2018 - 19:25

score 161 · Answer 8 · 2018-05-15 16:26:47

Prove the equality: $\det\left[\begin{smallmatrix} -2a &a+b &a+c \\ b+a&-2b &b+c \\ c+a&c+b &-2c \end{smallmatrix}\right] = 4(a+b)(b+c)(c+a)$

score 52 · Answer 9 · 2026-03-25 06:10:55

52

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Positive definiteness of a certain matrix product

Published on 25 Mar 2026 - 6:10

score 83 · Answer 10 · 2018-05-16 13:46:32

83

Views

Find all matrices A such as $|\det(A)| = \prod_{i=1}^n\left( \sum_{i=1}^n |a_{i,j}| \right)$

Published on 16 May 2018 - 13:46

score 84 · Answer 11 · 2018-05-17 14:39:42

84

Views

Equality of determinants of two square matrices

Published on 17 May 2018 - 14:39

score 186 · Answer 12 · 2018-05-17 23:40:08

186

Views

How to prove that $\det \left(\begin{array}{cc} 0 & A\\ -B & I \end{array}\right) = \det(AB) $

Published on 17 May 2018 - 23:40

score 63 · Answer 13 · 2026-03-25 23:42:26

63

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Finding an orthogonal matrix $P$ of the quadric $3x^2+3z^2-4xy-8xz+4yz=1$

Published on 25 Mar 2026 - 23:42

score 234 · Answer 14 · 2018-05-19 06:49:24

234

Views

Finding the determinant given the determinant of matrices.

Published on 19 May 2018 - 6:49

score 117 · Answer 15 · 2018-05-20 06:12:55

117

Views

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

Published on 20 May 2018 - 6:12

List Question

Proving the determinant of this matrix is $0$: $\left(\begin{smallmatrix}2&1&0&5\\-1&1&1&6\\5&1&-1&4\\5&1&3&0\end{smallmatrix}\right)$

Prove that the set of $n \times n$ matrices with determinant $1$ is unbounded closed with empty interior in $\mathbb{R}^{n^{2}}$.

If $\lambda$ is an eigen value of an orthogonal matrix $A$, then show that $\frac{1}{\lambda}$ is also an eigen value of $A$

Prove: Let $ A\in\mathsf{Mat}(2\times 2, \mathbb{R})$. If $ \det(A)$ is zero, then there exist a $ \mu\in\mathbb{R}$, so that $ \mu A = A^2$.

Determinant and solution of equations

Change negative area of triangle into positive area!

Calculate the determinant of this $5 \times 5$ matrix

Prove the equality: $\det\left[\begin{smallmatrix} -2a &a+b &a+c \\ b+a&-2b &b+c \\ c+a&c+b &-2c \end{smallmatrix}\right] = 4(a+b)(b+c)(c+a)$

Positive definiteness of a certain matrix product

Find all matrices A such as $|\det(A)| = \prod_{i=1}^n\left( \sum_{i=1}^n |a_{i,j}| \right)$

Equality of determinants of two square matrices

How to prove that $\det \left(\begin{array}{cc} 0 & A\\ -B & I \end{array}\right) = \det(AB) $

Finding an orthogonal matrix $P$ of the quadric $3x^2+3z^2-4xy-8xz+4yz=1$

Finding the determinant given the determinant of matrices.

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

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