joint distribution of the sample mean and variance

suppose that the random variables x1,x2, and x3 are i.i.d., and that each had a standard normal distribution. also suppose that

y1= .8x1 + .6x2

y2= [sqrt.(2)]*(.3x1-.4x2-.5x3)

y3= [sqrt.(2)]*(.3x1-.4x2-.5x3(

find the joint distribution of y1, y2, y3.

i feel like this should be simple but i have no idea how to do it. my book says the joint distribution is 1/detA * the joint distribution of the inverse of A * y. No idea how to start this problem any help would be great