# Midterm 1 Solutions - Name Section Number 110.201 Linear...

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Name:Section Number:110.201 Linear AlgebraFALL 2013MIDTERM EXAMINATION SolutionsOctober 11, 2013Instructions:The exam is7pages long, including this title page. The number of points eachproblem is worth is listed after the problem number. The exam totals to one hundred points. Foreach item, pleaseshow your workorexplainhow you reached your solution. Please do all thework you wish graded on the exam. Good luck !!PLEASE DO NOT WRITE ON THIS TABLE !!ProblemScorePoints for the Problem130230315425TOTAL100Statement of Ethics regarding this examI agree to complete this exam without unauthorized assistance from any person, materials, ordevice.Signature:Date:
please show all work, explain your reasons, and state all theorems you appeal to1Question 1.[30 points] For the systemx-y+ 3z= 1,y=-2x+ 5, 9z-x-5y+ 7 = 0,do the following:(a)Write the system in the matrix formAx=b, forx=xyz.Strategy:Reorder the equations to line up the variables and then dig out the matrixA.
(b)Write out the augmented matrix for this system and calculate its row-reduced echelonform.
2please show all work, explain your reasons, and state all theorems you appeal to(c)Write out the complete set of solutions (if they exist) in vector form using parametersif needed.Strategy:Use the resulting equations form the row-reduced echelon form of the augmented matrixto construct the solutions set. For each free-variable, associate a parameter and then write the othervariable in terms of the free variable. Then create a vector version.