# Matrix equations solving

can you explain me the easiest way for solving this matrix equation? I have this matrix:

a={{-4,1,3,0},{-2,7,1,-1},{1,-1,9,-3},{-1,0,5,-10}

and the Equation is:

2a-x+IdentityMatrix==0

Where x is the Unknown Matrix

or the better question apart from this upper exercise would be, how can i solve matrix equations that have this form A+X=...(0, or any other matrix)

• So, try replacing x with 2 a + IdentityMatrix... Jun 12, 2016 at 15:18
• I know, thats the "common way", but is there like a command like at the polynomials for example: Solve[x+1==0,x] but just for matrix solving? Jun 12, 2016 at 15:21
• Array[x, {4,4}] /. Solve[Flatten[ Thread /@ Thread[2 a - Array[x, {4, 4}] + IdentityMatrix == 0]], Flatten@Array[x, {4, 4}]] or Solve[Flatten[ Table[2 a[[i, j]] - x[i, j] + Boole[i == j] == 0, {i, 4}, {j, 4}]], Flatten[Array[x, {4, 4}]]] Jun 12, 2016 at 16:14

The following is a general technique, using Solve
a = {{-4, 1, 3, 0}, {-2, 7, 1, -1}, {1, -1, 9, -3}, {-1, 0, 5, -10}};