Hint: It is quite possible that as a beginner you cannot see through this for a quick
Question:
Hint:
It is quite possible that as a beginner you cannot see through this for a quick solution, if so, you can solve the equation via solving two triangular equations to get the final solution: First solve the outer lower triangular equation, then solve the inner upper triangular equation. (review the lecture/slides to find out the details.)
After you get the solution, then compare it with the solutions in (I) and (II) to see if you can discover some interesting connection among the solutions.
Even if you can see through the main structure and can get a solution quickly, it is still highly recommended that you solve for the solution step by step as mentioned above, then use the solution you get to double check if your insight is correct or not.
(The correct insight is related to the linearity of a linear transformation or operator. Thanks to linearity, for any matrix AA, if we know Ax=bAx=b has a solution xx, then for any fixed scalar cc, the equation Ax = c*b Ax=c∗b must have a solution c*xc∗x because A*(c*x) = c*Ax = c*b.A∗(c∗x)=c∗Ax=c∗b.)