Ispit iz Primjene Softwarea Mathematica 24 januar 2008.

Zadatak 1.

Q = {{3 a, 2, -1, 2}, {6, 1, 5 - a, 11 * a}, {-5, -1, 6 a, 17}, {-1, 3, 0, 2}}

{{3 a, 2, -1, 2}, {6, 1, 5 - a, 11 a}, {-5, -1, 6 a, 17}, {-1, 3, 0, 2}}

MatrixForm[Q]

( 3 a     2       -1      2     )            6       1       5 - a   11 a            -5      -1      6 a     17            -1      3       0       2

Det[Q]

555 + 1009 a - 255 a^2 - 594 a^3

MatrixForm[Transpose[Q]]

( 3 a     6       -5      -1    )            2       1       -1      3            -1      5 - a   6 a     0            2       11 a    17      2

temp = 2Q . Q * 3Q - 4 * IdentityMatrix[4]/.a1 ;

X = Inverse[temp] . {1, 2, 0, -2}

{104678035/5252364872, -265844221/5252364872, -107897181/656545609, 37447751/2626182436}

SporednaDijagonala[A_] := Module[{zbir, n}, zbir = 0 ; n = Length[A] ;  ...  = 1, i≤n, i ++, zbir = zbir + A[[n - (i - 1), i]] ] ; zbir]

SporednaDijagonala[Q]

5 - a



Zadatak 2.

MojRest[lista_, n_] := Module[{temp}, temp = {} ; For[i = n + 1, i≤Length[lista], i ++, temp = Append[temp, lista[[i]]] ] ; temp]

MojRest[{1, 2, 3, 4, 5}, 3]

{4, 5}

mojAppend[lista_, elem_] := Module[{i, ret, n}, n = Length[lista] ; ret = Tabl ... a[[i]], {i, 1, n} ] ; ret[[n + 1]] = elem ; Return[ret] ] 

mojAppend[{1, 2, 3, 4}, 5]

{1, 2, 3, 4, 5}

Zadatak 3.

rotiraj[xt_, yt_, alfa_] := Module[{}, Return[{{Cos[alfa], -Sin[alfa]}, {Sin[alfa], Cos[alfa]}} . {xt, yt}] ]

temp = Table[Null, {20}] ; 

For[i = 0, i<20, i ++, temp[[i + 1]] = ParametricPlot[rotiraj[Cos[5 * t], Sin[3 * t], (i/20) * Pi], {t, 0, 2 Pi} ] ]

Show[temp]

[Graphics:HTMLFiles/rjesenjaIspitPrimjena1_27.gif]

⁃Graphics⁃



Ispit iz Primjene Softwarea Mathematica 24 januar 2008.

Zadatak 1.

Q = {{1, 2 a, 0, 1}, {3, 1 - a, 5, 11 * a}, {3, 1, 6, 7}, {0, 2, 0, a}}

{{1, 2 a, 0, 1}, {3, 1 - a, 5, 11 a}, {3, 1, 6, 7}, {0, 2, 0, a}}

MatrixForm[Q]

( 1       2 a     0       1     )            3       1 - a   5       11 a            3       1       6       7            0       2       0       a

Det[Q]

76 - 131 a - 12 a^2

MatrixForm[Transpose[Q]]

( 1       3       3       0     )            2 a     1 - a   1       2            0       5       6       0            1       11 a    7       a

temp = Inverse[Q] ; MatrixForm[temp]

(                 2                  2                     2                         2 ...    2           76 - 131 a - 12 a      76 - 131 a - 12 a    76 - 131 a - 12 a     76 - 131 a - 12 a

Solve[Det[Q] 0, a]

{{a1/24 (-131 - 20809^(1/2))}, {a1/24 (-131 + 20809^(1/2))}}

SporednaDijagonala[A_] := Module[{zbir, n}, zbir = 0 ; n = Length[A] ;  ...  = 1, i≤n, i ++, zbir = zbir + A[[n - (i - 1), i]] ] ; zbir]

SporednaDijagonala[Q]

5 - a




Zadatak 2.

MojTake[lista_, n_] := Module[{temp}, temp = {} ; For[i = 1, i<n, i ++, temp = Append[temp, lista[[i]]] ] ; temp]

MojTake[{1, 2, 3, 4, 5}, 3]

{1, 2}

mojPrepend[lista_, elem_] := Module[{lista1, n, i}, n = Length[lista] ; lista1 ... 1]] = lista[[i]], {i, n} ] ; lista1[[1]] = elem ; lista1] 

mojPrepend[{1, 2, 3, 4}, 5]

{5, 1, 2, 3, 4}



Zadatak 3.

rotiraj[xt_, yt_, alfa_] := Module[{}, Return[{{Cos[alfa], -Sin[alfa]}, {Sin[alfa], Cos[alfa]}} . {xt, yt}] ]

temp = Table[Null, {20}] ; 

For[i = 0, i<20, i ++, temp[[i + 1]] = ParametricPlot[rotiraj[Sin[3 * t], Sin[5 * t], (i/20) * Pi], {t, 0, 4 Pi} ] ]

Show[temp]

[Graphics:HTMLFiles/rjesenjaIspitPrimjena1_56.gif]

⁃Graphics⁃


Created by Mathematica  (February 4, 2008)