18.06 Spring 2012 Problem Set 10 (not handed in/not graded)
This short extra problem set is not to be handed in. The problems are meant to help you
learn about linear transformations. The textbook problems are out of the 4th edition.
1. Do Problem 30 from
Solution Set 7, 18.06 Fall '11
1. Suppose
equal to
n > 1.
1 or 1
Prove that the determinant of an
n
by
n
matrix with every entry
is even.
Solution. Consider the big sum formula for computing the determinant. It will have
n!
n! permutations), each one equa
Solution Set 5, 18.06 Fall '11
1. Take two connected graphs
union be
C
A
and
(i.e. a big graph with
(a) What is the rank of
Solution. If
matrix of
C
R
and
C 's
S
B
A
with
and
B
a
and
b
vertices respectively.
Let their
as two disjoint parts).
adjacency mat
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