## Solutions vs Answers

for David L Ragozin's sections of Math 308, Spring 2004
• A solution to a problem should:
• Supply reasons or explanations or other notes to clarify the work presented.
• Demonstrate understanding of  the methods involved.
• Communicate what has been done and why:
• Any written solution, when read by you, other classmates, the instructor or grader,  will lead the reader to say `I understand how that was done', based on what is written.
• Numerical, or yes/no answers,  like the answers at the back of the book are not solutions.
Here is an example of a  typical linear algebra problem with an answer, a "professionals" solution and  then a solution in the style of this class.
Find numbers x,y which satisfy the equations:
E1 :   x + 2y =  1
E22x + 7y = -1

An answer :   x = 3 , y = -1.
A professionals solution : Gaussian elimination yields    x = 3 , y = -1.
A solution:

Subtract 2 * E1  from E2 to eliminate x, yielding
E1 :    x + 2y =  1
E'2 :                3y = -3
Divide E'2  by 3 to solve for y:
E1 :    x + 2y =  1
E''2 :            y = -1
Subtract 2 * E''2  from E1 to eliminate y, yielding the solution
E1   :    x    =  3
E'''2 :                y = -1

Note that the answer provides no reasons, explanations.  Although a reader who knows something about equations may be able to check the answer.