University of the District of Columbia Linear Algebra Questions

Please see the attachment for the questions

Please see the attachment for the questions Answer all questions, clearly showing the steps leading to your
solutions.
(Total points = 60)
1. Each of the differential equations (a), (b) and (c), can be
solved using at least two methods selected appropriately from
the following list of techniques introduced in chapter one of
your textbook : separable, linear, Bernoulli, homogeneous,
and exact. Solve each equation stating and using two different
methods selected from the given list and show that the two
solutions are equivalent. (10 points each)
(a)
dy
dic
+3y
y-3.0
(6)
2xy+2.3
c2+1
(c)
xy3 – – sy
do
2. Find a general solution for the following differential
equation : (10 points)
dy
dr
c2
2xy + y2
3. Solve the initial – value problem : (15 points)
6y(4) + 5y(3) + 254″ + 20y + 4y = 0,
y(0) = 1, y'(0)=
= =
1, y”(0) = 0, y(3)(0) = 2
4. The square matrix Ais said to be orthogonal if AT = A-1.
What are the posible values of det(A)?
(Justify your answer) (5 points)