- Look again at Fig. FE-9. This time, imagine two straight lines, one passing through
pointsP and S, and the other passing through lines Q and R. Consider the two-by-two
system of linear equations represented by these lines. This system has
(a) one solution.
(b) two solutions.
(c) three solutions.
(d) four solutions.
(e) infinitely many solutions.
- Imagine a three-by-three linear system of equations, each of which is in the following
form:
ax+by+cz=d
where a,b,c, and d are constants, and x,y, and z are variables. Now suppose that the
following matrix represents this system:
2006
0 − 3 012
0050
This matrix is in
(a) linear form.
(b) dependent form.
(c) diagonal form.
(d) unit diagonal form.
(e) redundant form.
- The matrix shown in Question 101 contains enough information so that we can infer
the solution to the linear system it represents. How can that solution be expressed as
an ordered triple of the form (x,y,z)?
(a) (3, −4, 0)
(b) (6, 12, 0)
(c) (2, −3, 5)
(d) (8, 9, 5)
(e) (12, −36, 0)
- Suppose we are trying to solve a three-by-three linear system using matrices. We are
sure we haven’t made any mistakes along the way. We come up with this matrix:
77728
1114
− 15 − 15 − 15 − 60
Final Exam 571
