vrije Univcrsitoi
te
, m amsterdam
Faculty of Economics and Business Administration
Exam: BM1-2 Business Mathematics - BK
Code: GIl'iKWU
Coordinator: K van den Iloeven
Date: December 20. 2011
Time: 12.00 -• 14.00
Duration: 2 hours
Calculator allowed: Yes
Graphical calculator allowed: No
Number of Quest ions: 5
Type; of questions: Open
Answer in: Dutch or English
Remarks You may keep the questions.
Credit score: lfl b c 'la b •An b 4« b c 5a b c start
5 8 6 9 8 8 8 10 4 6 4 4 10 10
Grades: The grades will be made public on: January 16,2012
Inspection: Thursday January 26.2012 at 12.50 - 13.20
Room will be announced later.
Number of pages: 5 (including front page and formula sheet
Good luck and success!
, Business Mathematics 1-2
The use of approved calculators is allowed for making this exam, but it will not be of any
help since we are not interested in just the answers, but in your ability to formulate the
full path of logical steps that lead to the solution. It is on this aspect that your work will
be judged.
For instance: |\/3 and |e~3/2 are perfectly acceptable outcomes of calculations, but
6%+y should be simplified to 2y.
question 1
(a) Let A= ( r 2 ) anc^ ^ ^ ^e tne transpose of A.
For what values of r is the matrix A denned?
Also calculate the matrix product AA' .
(b) Let x= ( Xl ) be an unknown (2 x l)-vector. Solve the following set of linear
equations for all values of a :
(l A-a)\x\ ) \l) •
(c) Let B=( ^ \ ) ,C=( J J j ,D=( j Mand let Xbe an unknown
(2 x 2)-matrix.
Solve X from the following matrix equation: XC"1 = B + D.
question 2
3
(a) Calculate t (x2 +- - e2*] dx
1
(b) Calculate g in the point (3,1) of the curve x2y - xy2 + 2>xy = 15.
te
, m amsterdam
Faculty of Economics and Business Administration
Exam: BM1-2 Business Mathematics - BK
Code: GIl'iKWU
Coordinator: K van den Iloeven
Date: December 20. 2011
Time: 12.00 -• 14.00
Duration: 2 hours
Calculator allowed: Yes
Graphical calculator allowed: No
Number of Quest ions: 5
Type; of questions: Open
Answer in: Dutch or English
Remarks You may keep the questions.
Credit score: lfl b c 'la b •An b 4« b c 5a b c start
5 8 6 9 8 8 8 10 4 6 4 4 10 10
Grades: The grades will be made public on: January 16,2012
Inspection: Thursday January 26.2012 at 12.50 - 13.20
Room will be announced later.
Number of pages: 5 (including front page and formula sheet
Good luck and success!
, Business Mathematics 1-2
The use of approved calculators is allowed for making this exam, but it will not be of any
help since we are not interested in just the answers, but in your ability to formulate the
full path of logical steps that lead to the solution. It is on this aspect that your work will
be judged.
For instance: |\/3 and |e~3/2 are perfectly acceptable outcomes of calculations, but
6%+y should be simplified to 2y.
question 1
(a) Let A= ( r 2 ) anc^ ^ ^ ^e tne transpose of A.
For what values of r is the matrix A denned?
Also calculate the matrix product AA' .
(b) Let x= ( Xl ) be an unknown (2 x l)-vector. Solve the following set of linear
equations for all values of a :
(l A-a)\x\ ) \l) •
(c) Let B=( ^ \ ) ,C=( J J j ,D=( j Mand let Xbe an unknown
(2 x 2)-matrix.
Solve X from the following matrix equation: XC"1 = B + D.
question 2
3
(a) Calculate t (x2 +- - e2*] dx
1
(b) Calculate g in the point (3,1) of the curve x2y - xy2 + 2>xy = 15.
