Question

How can i solve the matrix equation: 5Y - 2I₃ = Dt - (D+I₃)Y when D is a given 3x3 matrix? Dt (transpose of D)

| -5 2 3 |
| 2 -5 1 | = D
| 2 3 -5 |

Answer 1

See below.

Explanation:

`5Y - 2I₃ = D^top - (D+I₃)Y` or
`(5I_3+D+I_3)Y=D^top+2I_3` or
`(D+6I_3)Y=D^top+2I_3` or
`Y = (D+6I_3)^-1(D^top+2I_3) =((17/10,-13/5,2),(1/2,2,-3),(-19/10,1/5,2))`