DEPARTMENT OF MATHEMATICS
UNIVERSITY OF KANSAS
MATH 290 - Fall 2011 - Midterm exam
Your Name:
On this exam, you may use a calculator or computer, but no books or notes.
It is not sufficient to just write down the answers. You must explain how you arrived
at your answers and how you know they are correct.
1
(50)
2
(50)
3
(50)
4
(50)
5
(50)
Total (250)
2
(1) (50 points) Solve the linear system
x1 + 2x2 + x3 = −2
2x3 = −4
−2x1 − 4x2 + x3 = −2
You can use calculator, but state your extended matrix and the
reduced row matrix
3
(2) (50 points) A manufacturer produces three different models of a product,
which are shipped to two different warehouses. The number of units of model
i that are shipped to warehouse j are represented by aij in the matrix


200 300
A =  600 350 
250 400
The prices of the three models per unit are represented by
B = 12.50 9.00 21.50
Find the product BA and state what its entries represent.
You can use calculator
4
(3)
• (25 points) Use determinants to find the area of the triangle with the
vertices (1, 0), (5, 0), (5, 8).
• (25 points) Use determinants to find the equation of a line passing through
the points (1, 0) and (0, 1)
You can use calculator as long as you state the matrices you are
taking determinants of.
5




1 2 3
1 2
1
1  for some parameter
(4) (50 points) If A =  4 5 6  and B =  0 k
7 8 0
0 −1 k
k, determine det(AB), det(AT B), det(AB 10 A).
You can use calculators
6


1 a a
(5) (50 points) Let a be a parameter and A =  0 1 1  . Find A−1 and AAT .
0 0 1
You can use calculators