Page 17 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Show that if the linear equations and have the same solution set, then the equations are identical.
9.

Show that the elementary row operations do not affect the solution set of a linear system.
10.

For which value(s) of the constant k does the system
11.

have no solutions? Exactly one solution? Infinitely many solutions? Explain your reasoning.
Consider the system of equations
12.

Indicate what we can say about the relative positions of the lines , , and
when

(a) the system has no solutions.

(b) the system has exactly one solution.

(c) the system has infinitely many solutions.

If the system of equations in Exercise 12 is consistent, explain why at least one equation can be
13. discarded from the system without altering the solution set.

If in Exercise 12, explain why the system must be consistent. What can be said about
14. the point of intersection of the three lines if the system has exactly one solution?

We could also define elementary column operations in analogy with the elementary row operations.
15. What can you say about the effect of elementary column operations on the solution set of a linear

system? How would you interpret the effects of elementary column operations?

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