Linear Algebra and Dierential Equations
Problems
January 4, 2013
1
Linear Algebra
21. Solve the system of equations:
3x y + z = 4
x+y+z =4
x + y z = 3.
22. Find all 2 2 matrices A such that A2 is a scalar matrix. (That is, A2 is a
scalar multiple of the i
Vector Calculus Problems
January 4, 2013
1
Vector Calculus
Throughout, i, j , and k are the unit vectors along the x-, y -, and z -axes
respectively.
1. Let r(t) =
t, 2 t . Find r(1) and r (1).
/2
r(t)dt.
2. Let r(t) = 2 cos(t), sin(t), 2t . Find
0
3. Le