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[null,null,null,"          Powers of a Matrix"]
[]
[null,"                     This program lets you investigate the"]
[null,null,null,"         effects of successive powers An"]
[null,null,null,"               of a matrix A on a vector x0:"]
[null,null,null,"y1=Ax0,   y2 = Ax1 = A2x0,  y3 = Ax2 = A3x0, ..."]
[]
[]
[]
[]
["First enter the values for the matrix A:  "]
[null,null,null,null,0.3,-0.6]
[null,null,null,null,0.6,0.3]
[]
[]
["Enter the values for the initial vector X0:  ",null,null,null,null,null," "]
[null,null,null,null,5,null,null,null,null,"x0 =",5,"x1 =",{"$f":"Sheet2!F5","v":-2.5},"x2 =",{"$f":"IF(Sheet2!H4<=n,Sheet2!H1,\"\")","v":4.05},"x3 =",{"$f":"IF(Sheet2!J4<=n,Sheet2!J1,\"\")","v":-0.3450000000000002},"x4 =",{"$f":"IF(Sheet2!L4<=n,Sheet2!L1,\"\")","v":""},"x5 =",{"$f":"IF(Sheet2!N4<=n,Sheet2!N1,\"\")","v":""},"x5 =",{"$f":"IF(Sheet2!P4<=n,Sheet2!P1,\"\")","v":""}]
[null,null,null,null,-2,null,null,null,null,null,-3,null,{"$f":"Sheet2!F6","v":2.4},null,{"$f":"IF(Sheet2!H4<=n,Sheet2!H2,\"\")","v":-0.78},null,{"$f":"IF(Sheet2!J4<=n,Sheet2!J2,\"\")","v":2.1959999999999997},null,{"$f":"IF(Sheet2!L4<=n,Sheet2!L2,\"\")","v":""},null,{"$f":"IF(Sheet2!N4<=n,Sheet2!N2,\"\")","v":""},null,{"$f":"IF(Sheet2!P4<=n,Sheet2!P2,\"\")","v":""}]
[]
[null,"What is the highest power n (1 to 6)?",null,null,{"$f":"G20+1","v":3},62,2]
[]
[]
[null,"Click each item below for suggestions and investigations"]
[null,null,null,"   Item 1"]
[null,null,null,"   Item 2"]
[null,null,null,"   Item 3"]
[null,null,null,"   Item 4"]
[]
[]
[null,null,null,null,null,null,null,null,null," "]
[null,"Created by:  Sheldon P. Gordon"]
[null,"                     Farmingdale StateCollege"]
[null,"Development of this module was supported by the "]
[null,"NSF's Division of Undergraduate Education  "]
[null,"under grants DUE-0310123 and DUE-0442160."]

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[{"$f":"Sheet1!E12","v":0.3},2,null,{"$f":"Sheet1!$E$17","v":5},null,{"$f":"$A1*D1+$B1*D2","v":-2.5},null,{"$f":"$A1*F1+$B1*F2","v":4.05},null,{"$f":"$A1*H1+$B1*H2","v":-0.3450000000000002},null,{"$f":"$A1*J1+$B1*J2","v":4.2884999999999991},null,{"$f":"$A1*L1+$B1*L2","v":2.1901499999999992},null,{"$f":"$A1*N1+$B1*N2","v":6.0743249999999982}]
[{"$f":"Sheet1!E13","v":0.6},{"$f":"Sheet1!F13","v":0.3},null,{"$f":"Sheet1!$E$18","v":-2},null,{"$f":"$A2*D1+$B2*D2","v":2.4},null,{"$f":"$A2*F1+$B2*F2","v":-0.78},null,{"$f":"$A2*H1+$B2*H2","v":2.1959999999999997},null,{"$f":"$A2*J1+$B2*J2","v":0.45179999999999987},null,{"$f":"$A2*L1+$B2*L2","v":2.708639999999999},null,{"$f":"$A2*N1+$B2*N2","v":2.1266819999999993}]
[null,null,null,"v0",null,"v1",null,"v2",null,"v3",null,"v4",null,"v5",null,"v6"]
[null,null,null,0,null,1,null,2,null,3,null,4,null,5,null,6]
["plotting points:",null,0,{"$f":"D1","v":5},0,{"$f":"F1","v":-2.5},0,{"$f":"IF(H4<=n,H1,0)","v":4.05},0,{"$f":"IF(J4<=n,J1,0)","v":-0.3450000000000002},0,{"$f":"IF(L4<=n,L1,0)","v":0},0,{"$f":"IF(N4<=n,N1,0)","v":0},0,{"$f":"IF(P4<=n,P1,0)","v":0}]
[null,null,0,{"$f":"D2","v":-2},0,{"$f":"F2","v":2.4},0,{"$f":"IF(H4<=n,H2,0)","v":-0.78},0,{"$f":"IF(J4<=n,J2,0)","v":2.1959999999999997},0,{"$f":"IF(L4<=n,L2,0)","v":0},0,{"$f":"IF(N4<=n,N2,0)","v":0},0,{"$f":"IF(P4<=n,P2,0)","v":0}]
[]
["vector points",null,0,{"$f":"D1","v":5},0,{"$f":"F1","v":-2.5},{"$f":"IF(H$4<=n,G5,\"\")","v":0},{"$f":"IF(H$4<=n,H5,\"\")","v":4.05},{"$f":"IF(J$4<=n,I5,\"\")","v":0},{"$f":"IF(J$4<=n,J5,\"\")","v":-0.3450000000000002},{"$f":"IF(L$4<=n,K5,\"\")","v":""},{"$f":"IF(L$4<=n,L5,\"\")","v":""},{"$f":"IF(N$4<=n,M5,\"\")","v":""},{"$f":"IF(N$4<=n,N5,\"\")","v":""},{"$f":"IF(P$4<=n,O5,\"\")","v":""},{"$f":"IF(P$4<=n,P5,\"\")","v":""}]
[null,null,0,{"$f":"D2","v":-2},0,{"$f":"F2","v":2.4},{"$f":"IF(H$4<=n,G6,\"\")","v":0},{"$f":"IF(H$4<=n,H6,\"\")","v":-0.78},{"$f":"IF(J$4<=n,I6,\"\")","v":0},{"$f":"IF(J$4<=n,J6,\"\")","v":2.1959999999999997},{"$f":"IF(L$4<=n,K6,\"\")","v":""},{"$f":"IF(L$4<=n,L6,\"\")","v":""},{"$f":"IF(N$4<=n,M6,\"\")","v":""},{"$f":"IF(N$4<=n,N6,\"\")","v":""},{"$f":"IF(P$4<=n,O6,\"\")","v":""},{"$f":"IF(P$4<=n,P6,\"\")","v":""}]

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