Let a = 2 - i - 2j + k. Let b = x + yi + zj + wk. Work out a times b. This gives us the four equations:

2x + y + 2z - w = 1

-x + 2y -z - 2w = 0

-2x + y + 2z + w = 0

x + 2y - z + 2w = 0

The determinant of this coefficient matrix is not 0, so an inverse does exist. So solve the system.

-Dan