CSE 313
Midterm Examination
March 5, 2004
Question 1: {15 pts}
Consider the following system of linear equations:
21325
1334
423
−=−+−
=+++
−=+++
zyxw
zyxw
zyxw
Give the complete solution to this system – show your work.
Question 2: {15 pts}
If A is a square matrix such that (I – A) is nonsingular prove
that:
AAIAIA 11 )()( −− −=−
Question 3: {15 pts}
Suppose two matrices, A and B, are row equivalent, that is there
exists a nonsingular matrix P such that PA = B. Answer the
following questions about A and B. Explain your answer in each
case.
•Do A and B have the same column space ie does:
)()( BRAR =
•Do A and B have the same null space ie does:
)()( BNAN =
•Do A and B have the same row space ie does:
)()( TT BRAR =
•Do A and B have the same left hand null space ie does:
)()( TT BNAN =
Question 4: {15 pts}
