Math 601 Solutions to Homework 9
1. Let R be the tetrahedron in R3 with vertices (0, 0, 1), (0, 0, -1), (1, 1, 0), and (1, -1, 0). Evaluate the following integral: xy 2 dV
R
Answer: First, it helps to determine the 4 planes that determine the sides
Math 601 Solutions to Homework 10
1. Consider the vector field F(x, y) = (2x + 2y)i + (2x - y)j. (a) Find the parametric equations for the flow line of F beginning at the point (0, 5). (b) Find div(F). (c) Find rot(F). Answer: (a) We need to solve th
Math 601 Solutions to Homework 11
1. Consider the curve given by the following parametric equations: x = cos(t) and y = sin(2t)
Let D be the region inside this curve and to the right of the y-axis:
y
(a) Use Green's Theorem to compute
D
x2 dA.
(b
Math 601 Solutions to Homework 8
1. Find the distance between the following two lines: x 0 1 y = 1 + t 1 z 2 0 1 1 x y = -1 + t 1 0 3 z Answer: First, note that the two lines areparallel, since both lines 1 are in the directio
Math 601 Solutions to Homework 7
# $ . 1. Find a vector in the plane B" #B# $B$ oe ! that is orthogonal to the vector % Answer: The dot product of the vector aB" B# B$ b with a# $ %b must be zero. This gives the equation: #B" $B# %B$ oe ! We
Math 601 Solutions to Homework 6
1. Find the eigenvalues for each of the following matrices. For each eigenvalue, find a basis of the corresponding eigenspace. Determine whether the matrix is diagonalizable overthe complex numbers. 4 6 4 -2 -3 -4
Math 601 Solutions to Homework 4
1. Use row reduction to compute the determinants of the following matrices: 1 1 3 2 1 3 11 12 (a) A = 2 1 3 6 4 2 5 8 (b) B = Answer: (a) We row reduce the matrix: 1 1 3 2 1 3 11 12 - row 1 2 1