In Exercises 33 and 34, T is a linear transformation from R² into R2. Show that T is invertible and find a formula for T-1.
33. T(X1, X2) = (-5X1 + 9x2, 4x1-7X2)
34. T(X1,X2) = (2X18X2, -2X1+7X2)
35. Let T: R"R" be an invertible linear transformation. Ex- plain why T is both one-to-one and onto R". Use equations (1) and (2). Then give a second explanation using one or more theorems.
36. Suppose a linear transformation T : R" → R" has the prop- erty that T(u) = T(v) for some pair of distinct vectors u and v in R". Can T map R" onto R"? Why or why not?
37. Suppose T and U are linear transformations from R" to R" such that T(U(x)) = x for all x in R". Is it true that U(T(x)) = x for all x in R"? Why or why not?