# nee help completing problem from ma 140

Ultimately, you must be able to solve two-variable systems by hand, understanding that the power tools like the LAT can help you check your answers, and you should be able to solve 3-variable systems by hand as well.

For this exercise, you will solve four systems of linear equations from sections 8.2 and 9.2 and submit them by uploading your document.

While the TI-83 and other graphing calculators can handle up to 50 equations in 50 variables, as a practical matter, they are great for 5 equations in 5 unknowns, still beyond most students needs. However, it is not necessary to go out and buy one for this exercise.

At least one of the four problems assigned, will have an infinite number of solutions. You will want to see how LAT displays the final result when the case arises.

http://www.math.odu.edu/~bogacki/cgi-bin/lat.cgi

Chapter 8, Section 8.2 Practice Exercise Problems, #8 and #16:
On these two problems, first, perform the row operations following the Gaussian Elimination Procedure in the Linear Algebra Toolkit. Copy all your work and paste it into your submission document (MS Word or equivalent). Then, using the ad hoc method, take the same system and solve it by hand using the procedures of Example 2 on p. 809. Of course, you are expected to use one of your math editors in your submission document. The bracket symbol
{ is available to you using the MS Equation Editor for a system of three equations, and you can build this a number of ways in MathType. A similar bracket is available for the smaller system you create. Be sure you convert the reduced matrices back to a system of equations to identify your solution(s).

Your LAT solution and ad hoc solution will agree if you did both methods correctly.

Here is question #8:
8.2 #8.JPG

Here is question #16: 8.2 #16.JPG

Chapter 9, Section 9.2 Practice Exercise Problems: Check Point #1, (p. 879), and Checkpoint #2 (p. 882) On these two problems, it will be important to convert the reduced matrices back to a system of equations, so that if solutions exist, you can identify the set of solutions (infinite in number) defined by ordered triples with variables as needed. Follow Examples 1 and 2 carefully. You can use the Reduced Rwo Echelon button to get right to the simplified form of the matrix on these two.

Here is Checkpoint #1: 9.2 checkpoint 1.JPG

Here is Checkpoint #2: 9.2 checkpoint 2.JPG