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Worksheet Warmup Problems
The questions on this handout will help give an overview of where linear algebra begins.
Activity 0.1 .
(a)
Solve:
\begin{align*}
3x_1-2x_2\amp= 6\\
-x_1+x_2\amp= 1
\end{align*}
(b) Draw a graph of the solution set of the equation: \(3x_1-2x_2=6\text{.}\)
Hint . If a solution has \(x_1=a\text{,}\) what is \(x_2\) or viceversa?
(c) Draw a graph of the solution set of the equation: \(-x_1+x_2=1\text{.}\)
(d) Graph the solution sets from the two previous steps together. How does your answer to
part 0.1.a compare to your graph?
Activity 0.2 .
Solve:
\begin{align*}
2x_1-2x_2\amp=6\\
-x_1+x_2\amp=1
\end{align*}
Activity 0.3 .
Solve:
\begin{align*}
2x_1-2x_2\amp=-2\\
-x_1+x_2\amp=1
\end{align*}
Question 0.4 .
Wait…what just happened? Explain the results of the previous two activities. What do the graphs of the corresponding solution sets look like in relation to the graphs of the equations?
Question 0.5 .
What are the possible intersections of two lines? Clearly state your conjecture.
Throughout this course we will be doing many of the same things you did in the previous questions, but we will do them in a more general setting that will allow us to solve many new and old problems.
