Oppgaver til seminarene i ECON 3120/4120 Matematikk 2

i uken 8.�12. mars 2004

 

 

LA:��� 2.1.5,� 2.1.6, �2.1.8,� 2.2.4,� 2.3.2,� 2.3.3,� 2.4.2,� 2.4.5.

Eksamensoppgaver:�� 88(a),� 137.

 

 

Seminar problems in ECON 3120/4120 Mathematics 2

for the week 8�12 March 2004

 

 

�������� EMEA:�� 15.7.3,� 15.7.4, �15.7.6,� 15.7.8,� 15.8.2,� 15.8.4, and 2.4.2, 2.4.5 from LA.

�������� Exam problems:�� 88(a),� 137.

 

The problems 2.4.2 and 2.4.5 in LA are not in EMEA, so here are translations of them:

 

2.4.2:� Let� a = (�1, 2)� and� b = (3,1).

 

(a)� Calculate� ||a||,� ||b||,� and� ||a + b||.� Explain geometrically why� ||a|| + ||b||� does not equal� ||a + b||.

 

(b)� Calculate� a � b,� and check whether the Cauchy�Schwarz inequality holds.

 

2.4.5:� (a)�� Show that the vectors� (a,b)� and� (�b, a)� are always orthogonal to each� other.

 

(b)�� Show that� (a₁, a₂, a₃)� is orthogonal to� (a₂ � a₃, a₃ � a₁, a₁ � a₂)� for all values of� a₁,� a₂,� and� a₃.