let T: R^2 -> R^2 be a linear transformation define by
they are matrix they are both 2x1 incase you were wondering wth i did xD
show that T has an inverse
alright so im pretty sure i have to show that the LS has an inverse for T to have an inverse but i never really did any any question with a 1x2 matrix so i dont know how to do the inverse.. can someone help me out please
Do you remember way back in "precalculus" where you learned to find the inverse of a function? To find the inverse of y= f(x), swap x and y to get x= f(y) and solve for y. That gives y=
You can do a similar thing here: Since T(x,y)= (x+y, x-y)= (a, b), swapping (x,y) and (a,b) gives you (a+b, a- b)= (x,y) or a+ b= x, a- b= y. Solve those two equations for a and b.