Find a formula for T1 if Tx1 x2 8x1 x2 8x1 3x2 T1 x1 x2

Find a formula for T^-1 if T(x_1, x_2) = (8x_1 + x_2, 8x_1 - 3x_2) T^-1 (x_1, x_2) =

Solution

We have T(X) = T{(x₁,x₂)^T} = (8x₁ +x ₂, 8x₁-3x₂)^T where, X = (x₁,x₂)^T and A =

8

1

8

-3

Then A^-1 =

3/32

1/32

1/4

-1/4

Hence T^-1(X) = A^-1X = ( (3/32)x₁ +(1/32)x₂, (1/4)x₁-(1/4)x₂)^T

8	1
8	-3