## Finding Matrices From Matrix Equations

If a matrix appears as a variable in a polynomial equation then we can solve for it using techniquees similar to those used in ordinary algebra. In particular, we can factorise. If the polynomial in the matrix equals zero, then each factor equals zero and we can solve for the matrix. It should be noted though, that though the method below find solutions for the matrix, it does not find all solutions.

Example: Solve the matrix equation

Write the equation asand factorisethenor

Example: Solve the matrix equation

Write the equation asand factorisethenor

To see why this method does not find all solutions, consider the first equation

Ifthen