# Test 1 Study Guide

Make sure that you take time to practice all of the concepts we’ve gone over in class.

The test will focus on solving systems of linear systems, but there will also be questions on graphing linear inequalities.

For true and false questions, if your answer is false I will ask you to give a counter-example. For instance, take the statement: Every system of linear equations has a solution. This is false, and a counter-example is given by the system of equations $y=2x +1$ and $y=2x +5$. These lines are parallel, and so they never intersect. Thus, this system has no solution.

• Make sure you can graph a feasible set defined by a collection of linear inequalities
• Make sure you know what the elementary row operations.
• Make sure you can change a system of linear equations into an augmented matrix.
• Make sure you know what Gauss-Jordan Elimination means
• If a matrix has infinitely many solutions, make sure you can give at least 2 different solutions to the system using the general solution we compute with Gauss-Jordan Elimination
• Make sure you can perform matrix multiplication
• Make sure you can find the inverse of a matrix using Gauss-Jordan Elimination
• Make sure you can convert a system of linear equations into a matrix equation: $AX = B$.
• Make sure you know how use the inverse to find the solution.
• Make sure you can know that the solution to linear system is the same as the intersection of lines or planes
• You may want to draw different kinds of intersections we discussed in class: What kind of intersection of planes would give you infinite solutions? What about no solution?

Let me know if you have any questions, and good luck!