Let T: Rn → Rn be an invertible linear transformation, and let S and U be functions from Rn into Rn such that S(T(x)) = x and U (T(x)) = x for all x in R^n
Show that
U(v)= S(v) for all v in R^n

Required:
Compute S(v) and U(v).

Lee has $1.75 in dimes and nickels. the number of nickels is 11 more than the number of dimes. how many of each coin does he have?

Find the volume of the described solid.the solid lies between planes perpendicular to the x-axis at x = 0 and x=7. the cross sectionsperpendicular to the x-axis between these planes are squares whose bases run from the parabolay=-31x to the parabola y = 30/x.a) 441b) 147c) 864d) 882

Dexter read 11 science fiction books and 5 history books. lena read 9 science fiction books and 4 history books. compare the students’ ratios of science fiction books to history books. 1. determine the ratios’ form:    science fiction books to history books 2. write the ratios as fractions:    dexter: 115; lena: 94 3. rewrite with a common denominator. 4. compare. 5. answer the question. determine which shows the correct comparison of the ratios for this problem.