# Tagged Questions

1answer
38 views

### Invertible Matrices Proof

Given that B is an invertible matrix and $B^3 + B^4 + B^7 = I$, find an expression for $B^{-1}$ in terms of only $B$. (where $I$ is an identity matrix) $B$ is a matrix that is $n \times n$.
0answers
33 views

0answers
25 views

### Ax = B, group of columns of A.

Is there a matrix $A (n \times n)$ Over field $F$ and $b \in F^n$ has non-trivial solution to the equation $Ax=B$ ? Well, In the answer it is written that because that the set of the columns of ...
0answers
12 views

### Interpreting & Analysing a Transitional Matrix

How do you interpret such a problem Are we expect to add the rows, and that would be the one with larger number of goats in the long term. Therefore A(row 1) and b(row 2)... therefore the answer is ...
1answer
22 views

### If the first r columns of U are linearly independent, then so are the first r columns of A?

Let $U$ be a row echelon form of a square matrix $A$. If the first $r$ columns of $U$ are linearly independent, then should the first $r$ columns of $A$ be linearly independent? In my opinion, "Yes" ...
1answer
22 views

### Matrix $A$ with characteristic polynomial

Given: Matrix $A$ with characteristic polynomial $p(x) = (x+3)^2(x-1)(x-5)$ Also given: $\rho(A+2I) + \rho(A+3I) + \rho(A-5I) = 9$ (btw $\rho$ means rank of the matrix) Prove: $A$ is ...
1answer
45 views

0answers
28 views

### About Jordan-Chevalley decomposition

I have this problem: Let $K$ be a field. Let $J\in M_n(K)$ a Jordan matrix. Prove that there exists a diagonal matrix $D$ and a nilpotent matrix $N$ such that $J=D+N$ and $DN=ND$. I saw that this ...
1answer
41 views

### What does the question in the attached image mean?

here is a question : http://upimage.us/server/php/files/math%20Q%20%281%29.jpg what does " echelon form " mean ?
2answers
45 views

### If $AX=XA$ for all $X$, then $A = \alpha I$ for some $\alpha$

Let $A$ be a $2 \times 2$ real matrix such that $AX=XA$ for all $2 \times 2$ real matrices $X$. Show that $A= \alpha I$ for some $\alpha ∈R.$ I am absolutely stuck, i thought $X$ and $A$ are ...
2answers
35 views

### Minimizing Frobenius norm for two variables

I need to minimize squared Frobenius norm: $\|\mathbf{A} - \mathbf{x}\mathbf{y}^T\|_F^2$. Namely I need to prove that for this norm to reach minimum $\mathbf{x}$ should be eigenvector of ...
1answer
34 views

### Gram-Schmidt method and matrices help please!

How would I use the method of Gram-Schmidt to obtain an orthonormal basis for the column space of the matrix? Any help is appreciated!
2answers
41 views

### Gershgorin discs and norm of a matrix

Find a matrix, where the estimation of eigenvalues with the help of Gershgorin discs is a, the same as b, worse as the estimation with the help of the norm of the matrix ($||A||_\infty$) So, yes, ...
0answers
36 views

### problems on define set with polynomials

I'm trying to say set A is the set of nonnegative integers that not of this two forms $3x^2 + (6y-4)x - y\$ and $\ 3x^2 + (6y-2)x + (y - 1)$, for example: $4=3 \cdot1^2+(6 \cdot1-4) \cdot 1-1\$ is ...
1answer
24 views