Practice FINAl TEST 12/08/2008
1 A furniture manufacturer makes tabels, chairs, and sofas. In one month,
the company has available 300 units of wood, 350 units of labor, and
225 units of upholstery. The manufactuere wants a production schedule
for the month that uses all of these resources. The diFerence products
require the following amounts of the resources.
Table Chair Sofa
Wood
4
1
3
Labor
3
2
5
Upholstery
2
0
4
Set up and solve the system of equations to determine how much of each
product should be manufactured(using the LU decomposition).
2 The matrix B
p
2
3

1
3

1
3
2
3
P
is the inverse of A
p
2 1
1 2
P
(a) Verify that
u
1
= [1
,
1] and
u
2
= [1
,

1] are eigenvectors of both A
and B.
(b) Determine the eigen values of A and B. How are the eigenvalues of
A and B related?
3 Solve the secondorder diFerential equation by matrix form.(you must
±nd eigenvalues and eigenvectors.) The initial condition is
x
(0) = 10
, y
(0) =
10.
y
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 Spring '08
 FRIED
 Linear Algebra, Singular value decomposition, Orthogonal matrix, QR algorithm, Practice Final test

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