Asleen
  • Member for 5 years, 8 months
  • Last seen more than 2 years ago
  • Banja Luka, Republika Srpska, Bosnia and Herzegovina
2 answers
7 votes
398 views
6 bookmarks
We have matrix $A\in M_{n-1\times n}(\mathbb Z)$ so that the sum of entries in each row is zero. Prove that $\det(AA^T)=nk^2.$
3 answers
6 votes
550 views
3 bookmarks
Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
2 answers
4 votes
242 views
Prove that there is a base of $\mathbb R^4$ made of eigenvectors of matrix $A$
1 answers
4 votes
105 views
1 bookmarks
Let $A$=[$a_{ij}$]$_{n x n}$ where $a_{ii}$=$1$, $i=\overline {1,n}$, $a_{ij}=a\not=1, i\not=j$. Find $A^n$, $n\in \mathbb N$
2 answers
3 votes
140 views
1 bookmarks
$\{v_1,,...,v_{2014}\}$ are linearly independent. Find $\lambda$ so that $\{v_1+v_2,...,v_{2014}+\lambda v_1\}$ are also linearly independent.
1 answers
3 votes
65 views
Let $A$ and $B$ be matrices 2014 by 2014. Matrix $A$ is invertible. Is this equation possible: $AB-BA=A$?
4 answers
3 votes
95 views
Let $A$:$\mathbb R_5(x)$ $\rightarrow$ $\mathbb R_5(x)$ be linear map. Find matrix of operator $A$.
1 answers
3 votes
2k views
Prove that $\lambda_1^2$, $\lambda_1\lambda_2$ and $\lambda_2^2$ are eigenvalues of matrix $A$
2 answers
2 votes
146 views
Prove that the number: $z = \det(A+B) \det(\overline A-\overline B)$ is purely imaginary.
2 answers
2 votes
134 views
1 bookmarks
Prove (∀z∈ℂ\{1,-1} : |z|=1)(∃x∈ℝ) where z=(x+i)/(x-i)
1 answers
1 votes
100 views
1 bookmarks
Prove the following: $[1-\lambda \operatorname{sum}(A^{-1})][1-\lambda \operatorname{sum}(B^{-1})]=1$
1 answers
1 votes
52 views
Find the number of different magmas that have $A$ as its underlying set
2 answers
1 votes
198 views
Find subspace $T$ of space $\mathbb R^3$ so that $\mathbb R^3=S \oplus T$
1 answers
1 votes
59 views
Find the multiplicity of root $x=a$ of polynomial $Q(x)= \frac{1}{2}$*$(x-a)(p'(x)+p'(a))-p(x)+p(a)$
1 answers
0 votes
71 views
Orthogonal projection: Find vector $\overrightarrow w \in \Bbb R^2$ so that $\overrightarrow w$ is orthogonal to $\overrightarrow v$
1 answers
0 votes
71 views
1 bookmarks
Using the picture write down all values of $\sqrt[12]{z}$ and then find the main value of that number $z$.