Find the standard matrix of the linear transformation T:R3~R3 that reflects each vector through the plane x2 = x3. Solution rather it would be better to write y= z than x2 = x3 y = z is the plane through origin upon which the y and z coordinates are equal. for instance ( 1,2,2),(2,1,1) , ... are on this plane. the suitable linear transformation is T(x,y,z) = (x,y,y) or (x,z,z).

1. Find the two points, equidistant from the mean that would include the middle 95% of the
population. The population mean is 6 and the population standard deviation is 4.
Solution
x-6/4 =-1(0.025)=1.96
or,x=4*1.96+6=13.84
And other x = 2*6-13.84=-1.84