2. Find all eigenvalues and corresponding linearly independent
eigenvectors of A = [2 0 3 4] (Its a 2x2 matrix)
4. Find all eigenvalues and corresponding linearly independent
eigenvectors of A = [1 0 1 0 2 3 0 0 3] (Its's a 3x3 matrix)
6. Find all eigenvalues and corresponding eigenvectors of A =
1 2 3 0 1 2 0 0 1 .(Its a 3x3 matrix)
Find the characteristic equation and the eigenvalues (and
corresponding eigenvectors) of the matrix. 2 −2 5 0 3 −2 0 −1 2 (a)
the characteristic equation (b) the eigenvalues (Enter your answers
from smallest to largest.) (λ1, λ2, λ3) = the corresponding
eigenvectors x1 = x2 = x3 =
Let v1 be an eigenvector of an n×n matrix A corresponding to λ1,
and let v2, v3 be two linearly independent eigenvectors of A
corresponding to λ2, where λ1 is not equal to λ2. Show that v1, v2,
v3 are linearly independent.
4. Let r(?) = �?, 4 3 ? 3/2, ?2 �. (a) Find T, N, and B at the
point corresponding to ? = 1. (b) Find the equation of the
osculating plane at the point corresponding to ? = 1. (c) Find the
equation of the normal plane at the point corresponding to ? =
1
Let A = {1, 2, 3, 4, 5}. Find the inverse of the following
functions f: A→ A.
? = {(1,1),(2,3),(3,2),(4,4),(5,5)
? = {(1,5),(2,4),(3,2),(4,1),(5, 4)}
? = {(2,1),(3,4),(1,3),(4,1),(5, 2)}
Let A = (3, 4), B = (0, −5), and C = (4, −3). Find equations for
the perpendicular bisectors of segments AB and BC, and coordinates
for their common point K. Calculate lengths KA, KB, and KC. Why is
K also on the perpendicular bisector of segment CA?
4) Let ? = {2, 3, 5, 7}, ? = {3, 5, 7}, ? = {1, 7}. Answer the
following questions, giving reasons for your answers.
a) Is ? ⊆ ??
b)Is ? ⊆ ??
c) Is ? ⊂ ??
d) Is ? ⊆ ??
e) Is ? ⊆ ??
5) Let ? = {1, 3, 4} and ? = {2, 3, 6}. Use set-roster notation
to write each of the following sets, and indicate the number of
elements in...