Difference between revisions of "031 Review Part 2, Problem 11"

Revision as of 10:49, 10 October 2017

Consider the following system of equations.

x_{1}+kx_{2}=1

3x_{1}+5x_{2}=2k

Find all real values of $k$ such that the system has only one solution.

Foundations:
1. To solve a system of equations, we turn the system into an augmented matrix and
row reduce that matrix to determine the solution.
2. For a system to have a unique solution, we need to have no free variables.

Solution:

Step 1:

Step 2:

Final Answer:

@@ Line 10: / Line 10: @@
 {| class="mw-collapsible mw-collapsed" style = "text-align:left;"
 !Foundations: &nbsp;
+|-
+|'''1.''' To solve a system of equations, we turn the system into an augmented matrix and
 |-
 |
+::row reduce that matrix to determine the solution.
+|-
+|'''2.''' For a system to have a unique solution, we need to have no free variables.
 |}