Hey everyone... can some one explain to me why a vertical shear of 5 is NOT
Well the general form for a vertical shear is
but you can also tell by multiplying it by the basis vectors.
so you see the (1,0) vector does not change in the transformation, which should not be the case in a vertical shear. What this actually does is stretch everything out, because as you can see any y value is multiplied by 5, where in a shear transformation the magnitude of the y value changes according to the x value.
think about how something in a vertical sheer moves. It moves vertically, but the magnatitude of that movement is determined by its horizontal position (the farther it's x value is from zero the more its y value changes)
so [[1,0],[5,1]]*[x,y] = [x,(5*x+y)]
so while you could say 5 is in the 'x collumn', because it is multiplied by x, it is in the 'y row', because that product is added to y*1 to become the new y value.