Prof. A. Suciu
MTH 1230 -- Linear Algebra -- Fall 1997
Sample Quiz 3
- Let
Find:
- A basis for the row space of A.
- A basis for the column space of A.
- A basis for the null space of A.
- The rank of A.
- In each of parts first and second,
are the given vectors
independent or dependent? If they are independent, say why.
If they are dependent, exhibit a linear dependence relation
among them.
- Which of the given subsets of the vector space, M23,
of all matrices are subspaces? In each case,
give a reason for your answer.
- All matrices of the form
,
where b=a+c.
- All matrices of the form
,
where c>0.
- All matrices of the form
,
where a=-2c and f=e+2d.
- All matrices of the form
,
where a=2c+1.
- Which of the following sets of vectors span
?
In each case, give a reason for your answer.
- ,
,
.
- ,
,
,
.
- ,
,
,
.
- ,
,
,
,
.
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Created by Alexandru Suciu, Mon Oct 27, 1997
alexsuciu@neu.edu
http://www.math.neu.edu/~suciu/mth1230/1230f97.sq3/index.html