- Covered today: (NOTE: this is not in the book) System of linear equations
and techniques for solving them.
- For Next time:
- 1.
- Determine whether , where is a parameter is a solution of
the linear system:
- 2.
- Solve the given linear system without matrix notation:
- 3.
- Find the value of such that the system
has a solution other than .
- 4.
- Find all values of such that the system
has no solution.
- 5.
- Show that the linear system
where , and are constants, has a unique solution if
.
Express this solution in terms of , and .
- 6.
- Solve each linear system by the Gauss-Jordan matrix elimination method and
by Gauss elimination:
- (a)
-
- (b)
-
- 7.
- List the possible row-reduced echelon forms of the matrix
- 8.
- Prove that if we multiply any equation of an arbitrary linear system by a
nonzero scalar, the resultant system is equivalent to the original one.
- 9.
- Given a system of linear equations in three variables with the augmented
matrix
for what values of is there no solution for the system? Is there any value of
for which there are infinitely many solutions?
Math 9 Fall 2000
2000-10-18