MA 114 test 1 fall 2015 - Test 1 Review MA 114-004 Fall...

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Test 1 ReviewMA 114-004Fall 2015Test 1 will cover sections 1.1-1.4, 2.1-2.5, and 3.1-3.2 in Finite Mathematics and itsApplications, Goldstein, Schneider, and Siegel, 11th Edition.TopicsEquations of linesGraphing linesGraphing linear inequalitiesFinding feasible set of a system of linear inequalitiesFinding the intersection point of a pair of linesAddition MethodSubstitution MethodGaussian and Gauss-Jordan eliminationSolving systems of at least 2 variables using the Gauss-Jordan method.Matrix inverseFinding inverse of 2×2 matrixFinding inverse of larger dimension using the Gauss-Jordan methodDetermining if an inverse existsLinear ProgrammingFinding optimal solution using the steps outlined in class1
Some Practice Problems1. Let 4x-16y= 20.(a) Write this linear equation in standard form.(b) Sketch the graph of this line.(c) Determine whether the following points are on the graph of this line:i.(1,-1)ii.(0,3)iii.(-3,-2)iv.(4,0)2. Graph the feasible set and find the coordinates of the vertices:10x+ 4y14x+ 3y8x0, y03. (2.2.26) Use any method to find all solutions of the system of linear equations:x-3y+z=5-2x+7y-6z=-9x-2y-3z=64. (2.2.23) Use any method to find all solutions of the system of linear equations:4x+5y=33x+6y=12x-3y=75. (2.4.13) For the following linear system,12x+2y=43x+16y=0(a) Write the matricesA,X, andB, for the associated matrix equationAX=B.(b) FindA-1.(c) UseA-1to solve the matrix equation; give the solutionxandy. Show your work!6. (2.5.10) LetA=100

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