Concordia University
Math 251
Class Test
October 2012
Instructor: C Cummins
Time: 75 mins
30 marks (30% of nal grade)
All solutions must include a reasoned explanation.
Q1 (6 marks)
a) Show that W1 = cfw_(a1 , a2 , a3 , a4 ) I 4 | 2a1 a2 3a3 = 0 is a subs
Concordia University
Math 251
Instructor: C Cummins
Class Test
Time: 75 mins
October 2013
30 marks (30% of nal grade)
All solutions must include a reasoned explanation.
Some general comments:
1 Some people used the technique of writing down the conclusion
Concordia University
Math 251
Instructor: C Cummins
Class Test
Time: 75 mins
October 2013
30 marks (30% of nal grade)
All solutions must include a reasoned explanation.
Q1 (6 marks)
Let M22 (I be the vector space of 2 2 matrices with real entries.
R)
a b
Math 251 Midterm
Concordia University
Instructor: J. Macdonald
Time: 75 minutes
October 14, 2014
All solutions must include a carefully written explanation.
1. [10 points] Let A and B be subsets of a vector space V .
(a) Prove that
span(A B) span(A) span(