Výpočet determinantu - cvičení (str. 42/cv. 3)

a)

(%i1) M:matrix([3,1,-2],[0,4,-5],[0,3,7]);

Result

(%i2) determinant(M);

Result

(%i3) A:submatrix(2,3,M,2,3); B:submatrix(1,M,1);

Result

(%i5) determinant(A); determinant(B);

Result

(%i7) determinant(A)*determinant(B);

Result

b)

(%i8) M:matrix([1,2,-2,5],[-3,1,0,-5],[0,0,1,3],[0,0,2,-2]);

Result

(%i9) determinant(M);

Result

(%i10) A:submatrix(3,4,M,3,4); B:submatrix(1,2,M,1,2);

Result

(%i12) determinant(A); determinant(B);

Result

(%i14) determinant(A)*determinant(B);

Result

c)

(%i15) M:matrix([5,-1,0,0],[2,5,0,0],[2,4,4,-2],[3,-2,9,-5]);

Result

(%i16) determinant(M);

Result

(%i17) A:submatrix(3,4,M,3,4); B:submatrix(1,2,M,1,2);

Result

(%i19) determinant(A); determinant(B);

Result

(%i21) determinant(A)*determinant(B);

Result

Str. 42/cv. 4:
Určete, pro která x je daná matice regulární:

(%i22) load(fourier_elim);

Result

a)

(%i23) A:matrix([x,4],[3,x+1]);

Result

(%i24) regularni:expand(determinant(A))#0;

Result

(%i25) fourier_elim(regularni,[x]);

Result

(%i26) singularni:expand(determinant(A))=0;

Result

(%i27) solve(singularni,x);

Result

b)

(%i28) B:matrix([x,x],[x,5]);

Result

(%i29) regularni:expand(determinant(B))#0;

Result

(%i30) fourier_elim(regularni,[x]);

Result

(%i31) singularni:expand(determinant(B))=0;

Result

(%i32) solve(singularni,x);

Result

c)

(%i33) C:matrix([x,1,3],[0,x,2],[2,1,4]);

Result

(%i34) regularni:expand(determinant(C))#0;

Result

(%i35) fourier_elim(regularni,[x]);

Result

(%i36) singularni:expand(determinant(C))=0;

Result

(%i37) solve(singularni,x);

Result

d)

(%i38) D:matrix([1,0,x],[2,1,1],[x,0,x]);

Result

(%i39) regularni:expand(determinant(D))#0;

Result

(%i40) fourier_elim(regularni,[x]);

Result

(%i41) singularni:expand(determinant(D))=0;

Result

(%i42) solve(singularni,x);

Result

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