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{"sheet":"goal seek and solver","index":3,"n_rows":3,"n_cols":4,"rows_kept":3,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
["x","y=100sin(x)+50cos(2x)"]
[0.28003891062464686,69.99999290595116,null,"this value of x was found using Goal Seek"]
[2,58.24756163938758,null,"this local maximum was found using Solver"]

{"sheet":"simultaneous eqs","index":4,"n_rows":6,"n_cols":7,"rows_kept":6,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
[null,null,null,"seed values","rhs produced","desired","squared diff."]
[null,"coefficients",null,"for x, y and z","by  seed values","rhs","between cols. E and F"]
[4,8,4,0,0,80,6400]
[2,1,-4,0,0,7,49]
[3,-1,2,0,0,22,484]
[{"$nulls":6},6933]

{"sheet":"s. eqs. formulas","index":5,"n_rows":6,"n_cols":7,"rows_kept":6,"cut":false,"hidden":false,"merged":[[1,0,1,2]],"flags":["formulas_cached_only"]}
[null,null,null,"seed values","lhs produced","required","difference between"]
["coefficients",null,null,"for x, y and z","by  seed values","rhs","lhs and rhs, squared"]
[4,8,4,0,0,80,6400]
[2,1,-4,0,0,7,49]
[3,-1,2,0,0,22,484]
[{"$nulls":6},6933]

{"sheet":"matrices","index":6,"n_rows":28,"n_cols":22,"rows_kept":28,"cut":false,"hidden":false,"merged":[],"flags":["formulas_cached_only"]}
[]
[null,null,null,1,2,3,null,3,6,9]
[null,3,"*",-4,5,-6,"=",-12,15,-18,null,null,null,"scalar multiplication"]
[null,null,null,0,0,9,null,0,0,27]
[]
[null,1,2,3,null,1,2,3,null,2,4,6]
[null,4,5,6,"+",3,2,1,"=",7,7,7,null,"matrix addition"]
[null,7,8,9,null,1,2,3,null,8,10,12]
[]
[null,1,2,3,null,1,3,null,10,14]
[null,4,5,6,"*",3,1,"=",25,35,null,null,null,"matrix multiplication"]
[null,7,8,9,null,1,3,null,40,56]
[]
[{"$nulls":4},1,2,3,null,-1.083333333333333,-0.5,0.5833333333333334]
[null,null,null,"the inverse of ",4,5,4,"is",0.6666666666666663,1,-0.6666666666666666,null,null,"matrix inversion"]
[{"$nulls":4},7,8,9,null,0.2500000000000001,-0.5,0.24999999999999997]
[]
[{"$nulls":4},1,2,3,null,1,7]
[null,null,null,"the transpose of ",7,8,9,"is",2,8,null,null,null,"matrix transposition"]
[{"$nulls":8},3,9]
[]
[{"$nulls":5},1,2,3]
[{"$nulls":4},"the determinant of ",4,5,4,"is",-12,null,null,null,"matrix determinant"]
[{"$nulls":5},7,8,9]
[]
[null,null,4,8,4,null,null,80,null,null,0.012820512820512824,0.1282051282051282,0.23076923076923073,{"$nulls":4},6.999999999999999,null,null,null,"system of equations"]
[null,"A =",2,1,-4,null,"b =",7,null,"A-1 = ",0.10256410256410256,0.02564102564102564,-0.15384615384615383,null,null,"x = A-1 * b = ",null,4.999999999999999,null,null,null,"solved by matrix inversion"]
[null,null,3,-1,2,null,null,22,null,null,0.032051282051282055,-0.1794871794871795,0.07692307692307693,{"$nulls":4},3.0000000000000004]