Question

Although problems are categorized by topics, this should not be taken very seriously since
many problems fit equally well in several different topics.
Notation: We occasionally write M(n, F) for the ring of all n × n matrices over the field F, where
F is either R or C.

2. Which of the following sets of vectors are bases for R
2
?
a). {(0, 1), (1, 1)}
b). {(1, 0), (0, 1), (1, 1)}
c). {(1, 0), (−1, 0}
d). {(1, 1), (1, −1)}
e). {((1, 1), (2, 2)}
f ). {(1, 2)}

Answer 1

a and d