1
Homework for Oct 15
For the following matrices Aanswer the following
a) Compute rank(A), dim span(A) (dimension of the columns space), dim rowspan(A)
(dimension of the row space), dim N(A), and dimN(AT).
b) Find two different bases for span(A) (column space) and rowspan(A) (row space).
c) Find a basis for N(A) and N(AT).
d) Are the rows linearly independent? spanning? Are the columns linearly independent?
spanning?
If an answer to any of these questions is ’no’, show a certificate, i.e. if linearly dependent
a non-zero linear combination equal to the zero vector; if non-spanning a vector not in
the span.
e) In 2. only: What is the transition matrix for the change of basis between the two bases
of span(A) that you found in b)?
1.
A=
2 3 5 −1
3 1 4 2
−3−4−7 1
2.
A=
−3 2
−1 3
3 1