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.