When calculating the nullspace of a n x n matrix, after i have reduced the matrix to row echelon form, DO ALL MY PIVOTS HAVE TO BE 1 BEFORE i can distinguish the free variables, and then calculate the vectors that satisfy Ax=0?
Also, I just noticed your question is "why do the authors have 4m/2s," this is because they are trying to find the AVERAGE VELOCITY of the first straight portion of the graph. ie:
(4m-0m)/(2s-0s)= 4m/2s= 2m/s at point A (the half-way point of that portion of the line). Thats all this is. Then...
The point in question is point A. The graph of the line at point A is f(x)=2x; therefore, its derivative (ie: the slope of a line tangent to point A) is f(x)'=2+C. This shows the instantanious acceleration to be 2m/(s^2). Dont over think it.