Solving a matrix equation?

I'm trying to solve the following matrix equation using MATLAB:

AU + UB = C

A, B, and C are known matrices and I want to solve for the matrix U. A and B are square, symmetric, and tridiagonal. Does anyone have advice on how to use MATLAB to efficiently solve this system? Thank you for any help in advance!

[Worku Fufa]

40v+5i+0.5i2=0

85v+(i3+i2)4=0

i1=10+i2+i4

Answer 1

[Torsten]

Look at 5.1.10 under

http://www.math.uwaterloo.ca/~hwolkowi//matrixcookbook.pdf

for a solution.

Enter

help kron

to get information on how to form the Kronecker tensor product in MATLAB.

Best wishes

Torsten.

[Matt]

Thank you for your answer! While your solution works, I discovered that MATLAB has a straightforward command for solving this system - see my answer if interested.

Answer 2

[Matt]

For anyone who may stumble upon this in the future, turns out my system is the Sylvester equation. Its solution has been implemented in MATLAB starting in version 2014a:

http://www.mathworks.com/help/matlab/ref/sylvester.html

Answer 3

[Pramod Palayangoda]

1. Consider the following system of equations.

2𝒙𝟏 + 𝟓𝒙𝟐 + 𝟓𝒙𝟑 = 𝟓

4𝒙𝟏 − 𝒙𝟐 + 𝟐𝒙𝟑 = −𝟔

−𝟐𝒙𝟏 + 𝟑𝒙𝟐 − 𝒙𝟑 = 𝟏𝟏

i) Form a matrix for the coefficients of the above system and name it as A.

ii) Find the determinant of A.

iii) Find the inverse of A.

iv) Form a matrix for the right hand values and name it as B

v) Solve the above system.

Answer 4

[Karthikeyan S]

2𝒙𝟏 + 𝟓𝒙𝟐 + 𝟓𝒙𝟑 = 𝟓