Let"s have a 3xn matrice with the following properties:
The firs row of the matrice is 1,2,3,... ,n in this order.
The second and the third rows are permutations of the first.
Very important, that in each column thera are different entries.
How many matrices with thees properties are there?

The answer for 2xn matrices is well-known, but what is the answer for 3xn, or for kxn ( k<=n) ?

Let be the set of all matrices with at most two entries in each row equal to and all other entries equal to .
Determine the size of the set .
Here denotes the determinant of the matrix .

Let A \in \mathbb{R}^{n \times n} be a matrix such that A^2 = A and A \neq I and A \neq 0.

Problem:
a) Show that the only possible eigenvalues of A are 0 and 1.
b) What kind of matrix is A? (Hint: Think projection.)
c) Give a 2×2 example of such a matrix.

Hi everyone,

I was wondering whether when I tried to compute e^(2x2 matrix) and got the expansions of sinx and cosx with the method of discounting the constant junk whether it plays any significance. I am a UK student and none of this is in my School syllabus so I was just wondering…

A
matrix 2*2

A^2=3A+2i
A^3=mA+Li


i means identity matrix,

find constant m ، L

Show that if is an integer, then there exist invertible matrices with non-zero entries such that:


Edit.

Q) 1. Let be external direct sum of vector spaces and over a field .let and
show that
i) and is subspaces.
ii)

Q)2. Suppose . Let be the external direct sum of and . show that is isomorphic to under the correspondence

I face some trouble to solve this problems help me for understanding.
thank you.

Any idea?? Diff equational system combined with Matrix theory.
Consider the equation dX/dt=X^2, where X(t) is an n×n matrix satisfying the condition detX=0. It is known that there are no solutions of this equation defined on a bounded interval, but there exist non-continuable solutions defined on unbounded intervals of the form (t ,+∞) and (−∞,t). Find n.

Let be an integer and let be the set of all invertible matrices in which their entries are or . Let be the number of 's in the matrix . Determine the minimum and maximum values of in terms of , as varies over .

Find all matrices such that Edit: Proposed by Marian Vasile