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)