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

For this exercise, you will solve four systems of linear equationsfrom 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 50equations in 50 variables, as a practical matter, they are great for 5equations in 5 unknowns, still beyond most students needs. However, itis not necessary to go out and buy one for this exercise.

At least one of the four problems assigned, will have an infinitenumber of solutions. You will want to see how LAT displays the finalresult 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 theGaussian Elimination Procedure in the Linear Algebra Toolkit. Copy allyour work and paste it into your submission document (MS Word orequivalent). Then, using the ad hoc method, take the same system andsolve 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 submissiondocument. The bracket symbol

**{**isavailable to you using the MS Equation Editor for a system of threeequations, and you can build this a number of ways in MathType. Asimilar bracket is available for the smaller system you create. Be sureyou convert the reduced matrices back to a system of equations toidentify 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 twoproblems, it will be important to convert the reduced matrices back to asystem of equations, so that if solutions exist, you can identify theset of solutions (infinite in number) defined by ordered triples withvariables as needed. Follow Examples 1 and 2 carefully. You can use theReduced Rwo Echelon button to get right to the simplified form of thematrix on these two.

Here is Checkpoint #1: 9.2 checkpoint 1.JPG

Here is Checkpoint #2: 9.2 checkpoint 2.JPG