Problem 58787. Solve the matrix equation AXB + X + C = 0 for X

Created by Christian Schröder
Appears in Guess the Logic! II

Difficulty:Rate

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Let A, B, and C be square matrices of equal size, and let the matrix X be defined by the matrix equation
    A * X * B + X + C = 0
Please solve this equation for X. For instance, if
A = [1 2 ; 3 4];
B = [5 6 ; 7 8];
C = [9 10 ; 11 12];
then
X = [-1/2 5/3 ; -19/6 1];
solves the equation, as is easily checked. You may assume that A, B and C are such that a solution exists.

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Last Solution submitted on Jul 31, 2024

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ChrisR on 31 Jul 2023

I learned some math, and the solutions of Tim and Christian taught me three new commands.

Richard Zapor on 4 Aug 2023

The width and height are relatively new functions and I never heard of the Cat function used by Tim. Sadly virtually no one will learn of the Cat function.

Christian Schröder on 4 Aug 2023

> the Cat function used by Tim

That took me a moment to get, but I'll refer to it as that from now on.

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Problem 58787. Solve the matrix equation AXB + X + C = 0 for X

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Last 200 Solutions

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Problem Recent Solvers7

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Problem 58787. Solve the matrix equation AXB + X + C = 0 for X

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers7

Suggested Problems

More from this Author17

Problem Tags

Community Treasure Hunt

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