Problem 1
determine the area bounded by the curve
Explain your answer in detail:
Problem 2
Let U be an n x n upper triangular matrix such that
. For any t define
You will be asked to find the inverse of the matrix E(t) by looking for an
expression of the form which gives the inverse matrix. Set up a linear system to solve for c1, c2, c3.
a) Write the linear system that the coefficients c1, c2, c3 ought to satisfy
in the form Ax = b, and then solve for c1, c2, c3.
A =
b =
b) What is the inverse of E(t)?
E(t)^-1 =
EXPLAIN
c)Check if E(t)E(s) = E(t + s). If it is true derive this equation.
d)Define d/dtE(t) by differentiating each of the entries aij(t) of the
matrix E(t). Is it true that d/dtE(t) = UE(t)? If it is true, derive the equation.
a) Look up in a list of Taylor series of standard functions seen in calculus
and identify the entries that one gets if n ∞
b)
B(t)=