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[{"$nulls":3},"       Finding the Eigenvectors"]
[]
[{"$nulls":3},"   This DIGMath module lets you find the"]
[{"$nulls":3},"        eigenvectors of a 2 by 2 matrix A"]
[{"$nulls":3},"   geometrically by estimating the vector X"]
[{"$nulls":3},"       such that AX is a multiple of X."]
[]
[]
["          First define the matrix A =   ",{"$nulls":3},"using the sliders below:"]
[]
[{"$nulls":4},{"$f":"D15","v":1},{"$f":"D18","v":1}]
[{"$nulls":4},{"$f":"D21","v":-3},{"$f":"D24","v":-1}]
[]
["Enter the value for a (-5 to 5):  ",{"$nulls":5}," "]
[null,null,"a =",{"$f":"F15-5","v":1},62,6]
[{"$nulls":9},"Now create your trial vector X0  ="]
["Enter the value for b (-5 to 5):  "]
[null,null,"b =",{"$f":"F18-5","v":1},62,6]
[{"$nulls":10},"Enter the values for x (-5 to 5):  ",{"$nulls":5}," "]
["Enter the value for c (-5 to 5):  ",{"$nulls":11},"x =",{"$f":"(P20-50)/10","v":-0.3},62,47]
[null,null,"c =",{"$f":"F21-5","v":-3},62,2]
[{"$nulls":10},"Enter the values for x (-5 to 5):  ",{"$nulls":5}," "]
["Enter the value for d (-5 to 5):  ",{"$nulls":11},"y =",{"$f":"(P23-50)/10","v":-0.1},62,49]
[null,null,"d =",{"$f":"F24-5","v":-1},62,4]
[]
[{"$nulls":10},"X0 =",{"$f":"x0","v":-0.3},null,null,"X1= AX0 =",{"$f":"Sheet2!G6","v":-0.4}]
["Click each item below for suggestions and investigations",{"$nulls":10},{"$f":"y0","v":-0.1},{"$nulls":3},{"$f":"Sheet2!H6","v":0.9999999999999999}]
[{"$nulls":3},"   Item 1"]
[{"$nulls":3},"   Item 2",{"$nulls":7},{"$f":"IF(OR(Sheet2!F11=0,Sheet2!F12=0),\"\",IF(ABS(theta1-theta0)<0.01,\"That's virtually one of the two eigenvectors!\",\"\"))","v":""}]
[{"$nulls":3},"   Item 3"]
[{"$nulls":3},"   Item 4",{"$nulls":6},"The approximate eigenvalues are:  "]
[{"$nulls":11},"l1 =",{"$f":"IF(Sheet2!$D$16=1,Sheet2!B17,Sheet2!C17)","v":0},{"$f":"IF(Sheet2!$D$16=1,\"\",\"+ \"&TEXT(Sheet2!D17,\"0.00\")&\"i\")","v":"+ 1.41i"}]
[{"$nulls":11},"l2 =",{"$f":"IF(Sheet2!D$16=1,Sheet2!B19,Sheet2!C19)","v":0},{"$f":"IF(Sheet2!$D$16=1,\"\",\" - \"&TEXT(Sheet2!D17,\"0.00\")&\"i\")","v":" - 1.41i"}]
[]
["To access/download all the DIGMath Apps for College Algebra/Precalculus"]
["Click this link:",null,"DIGMath Modules for College Algebra and Precalculus"]
[{"$nulls":8}," "]
["Created by:  Sheldon P. Gordon   &   Florence S. Gordon"]
["                  Farmingdale State College      NYIT"]
["Development of this module was supported by the "]
["NSF's Division of Undergraduate Education  "]
["under grants DUE-0310123 and DUE-0442160."]

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[{"$f":"Sheet1!E11","v":1},2]
[{"$f":"Sheet1!E12","v":-3},{"$f":"Sheet1!F12","v":-1}]
[]
[]
["plotting points:",null,0,{"$f":"D1","v":0},null,null,0,0]
[null,null,{"$f":"x0","v":-0.3},{"$f":"y0","v":-0.1},null,null,{"$f":"a*x0+b*y0","v":-0.4},{"$f":"cc*x0+d*y0","v":0.9999999999999999}]
[]
["vector points",null,0,{"$f":"D1","v":0}]
[null,null,0,{"$f":"D2","v":0}]
[]
[null,null,"theta0 =",{"$f":"ATAN((D6-D5)/(C6-C5))","v":0.32175055439664224},null,{"$f":"C6-C5","v":-0.3}]
[null,null,"theta1 =",{"$f":"ATAN((H6-H5)/(G6-G5))","v":-1.1902899496825317},null,{"$f":"G6-G5","v":-0.4}]
[{"$nulls":5},"denoms:",{"$f":"IF(AND(Sheet2!F11<>0,Sheet2!F12<>0),\"OK\",\"NG\")","v":"OK"}]
[{"$nulls":5},"theta1-theta0:",{"$f":"IF(ABS(theta0-theta1)<0.01,\"OK\",\"NG\")","v":"NG"}]
[]
[null,"Reals","Complex",{"$f":"IF((a+d)^2-4*(a*d-b*cc)>0,1,-1)","v":-1}]
["lambda1 =",{"$f":"IF((a+d)^2-4*(a*d-b*cc)>0,((a+d+SQRT((a+d)^2-4*(a*d-b*cc)))/2),\"\")","v":""},{"$f":"IF((a+d)^2-4*(a*d-b*cc)>0,\"\",(a+d)/2)","v":0},{"$f":"IF((a+d)^2-4*(a*d-b*cc)>0,\"\",SQRT((-1)*((a+d)^2-4*(a*d-b*cc))))/2","v":1.4142135623730951}]
[]
["lambda2 =",{"$f":"IF((a+d)^2-4*(a*d-b*cc)>0,((a+d-SQRT((a+d)^2-4*(a*d-b*cc)))/2),\"\")","v":""},{"$f":"IF((a+d)^2-4*(a*d-b*cc)>0,\"\",(a+d)/2)","v":0},{"$f":"IF((a+d)^2-4*(a*d-b*cc)>0,\"\",-SQRT((-1)*((a+d)^2-4*(a*d-b*cc))))/2","v":-1.4142135623730951}]

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