Linear Algebra 
Test #1

March 21, 2003

Name____________________ 
R. Hammack

Score ______

(1) (9 points) This problem concerns the vectors , , .
(a)
(b)
(c) Two of the vectors u, v, and w are orthogonal.
Which two, and why?
(2) (10 points) Find the distance between the point in
and the plane .
(3) (10 points) Find the solution of the following linear system. Write
the solutions in vector form.
(4)
(a) (10 points) Consider the set of vectors in
. Is
this a line or a plane? If it is a line, write its equation in vector
from. If it is a plane, write its equation in normal form.
(b) (10 points) Consider the set of vectors in
. Is
this a line or a plane? If it is a line, write its equation in vector
from. If it is a plane, write its equation in normal form.
(5) (10 points) Suppose A, B and X are invertible
nbyn matrices. Solve the following equation for X.
(6) This problem concerns the vectors ,
,
.
(a) (10 points) Are these vectors linearly independent or linearly dependent?
Show your work.
(b) (5 points) Is the span of these vectors equal to ? Why
or why not?
(7) (10 points) Suppose A is a 3by4 matrix. Are the columns
of A linearly independent, linearly dependent, or is there not enough
information to say? Explain.
(8) (10 points) This problem concerns the invertible matrix
(a) Find .
(b) (6 points) Use your answer to part (a) above to find a
solution to the equation .