Question

The set of all X∈R^{2 × 2} that satisfies AX−XA =
[_{00}^{0 0}], where A is a constant 2 × 2 matrix.
(The exact values of the entries of A don’t matter.)

Answer #1

Given a matrix system AX = B as below, where A is a 4 x 4
matrix as given below
A:
2
1
0 0
1
2
1 0
0
2
4 1
0
0
1 3
B:
0
-1
3
-1
Solve for all 4 X values using TDMA
algorithm
First identify the a, d, c and b values for each row, and then
find P’s and Q’s and finally determine X’s.

Find the fundamental matrix solution for the system x′ = Ax
where matrix A is given. If an initial condition is provided, find
the solution of the initial value problem using the principal
matrix.
A= [ 4 -13 ; 2 -6 ]. , x(o) = [ 2 ; 0 ]

Let V be the set of polynomials of the form ax + (a^2)(x^2), for
all real numbers a. Is V a subspace of P?

Find the matrix A in the linear transformation y =
Ax,where a point x = [x1,x2]^T is projected on the x2 axis.That
is,a point x = [x1,x2]^T is projected on to [0,x2]^T . Is A an
orthogonal matrix ?I any case,find the eigen values and eigen
vectors of A .

y[n] =b(ax[n] +x[n-1]+ax[n-2]) where a&b >0.
Find the frequency response of the system H(e^jw). Determine the
values of a & b, if the magnitude response of the filter at w =
0 is 1 and at w =pi÷2 is 0.5.
thanks

1. Consider the set U={(x,y) in R2| -1<x<1 and y=0}. Is U
open in R2? Is it open in R1? Is it open as a subspace of the disk
D={(x,y) in R2 | x^2+y^2<1} ?
2. Is there any subset of the plane in which a single point set
is open in the subspace topology?

Exercise 9.1.11 Consider the set of all vectors in R2,(x, y)
such that x + y ≥ 0. Let the vector space operations be the usual
ones. Is this a vector space? Is it a subspace of R2?
Exercise 9.1.12 Consider the vectors in R2,(x, y) such that xy =
0. Is this a subspace of R2? Is it a vector space? The addition and
scalar multiplication are the usual operations.

formulate the following as a mixed-integer program
the set X\{x*} where X={x in Z^n. Ax<=b} and x* in X

Solve the IVP x''+ax=b+e-ct, x(0)=x'(0)=0, a, b, c
all positive parameters. Does your solution approach a constant as
t goes to infinity? If not, why not?

Let f(x) = x 2 + ax + 2. Find the values of a such that f(x)
> 0 for every x.

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