matlab实验三.doc

1. 1) >> a1=[1 ;0; 0]; a2=[0 ;1; 1]; a3=[1 ;0; 1]; A=[a1,a2,a3] A= 101010011 >> rank(A) ans =3 {a1,a2,a3} is spanning set for Or >> det(A) ans =R3?1, because the rank ofA equals to 3. 1 {a1,a2,a3} is spanning set for 2)R3?1, for the determinant ofA is not zero. >> a1=[1 ;0; 0]; a2=[0 ;1; 1]; a3=[1 ;0; 1]; a4=[1 ;2; 3]; A=[a1,a2,a3,a4] ; rref(A) ans =100001020011 The result shows that {a1 a2 a3} is spanning set for Or >> A1=A(:, 1:3) A1 = R3? >> rank(A1) ans =3 >> rank(A) ans =3 The result shows that {a1 a2 a3} is spanning set for 3)R3?1. >> a1=[2 ;1 ;- 2]; a2=[3 ;2 ;- 2]; a3=[2 ;2; 0]; A=[a1,a2,a3] A= >> rref(A) ans =10-2012000 They are not spanning sets for Or >> det(A) ans =R3?1, because there are less than 3 independent vectors. 0 They are not spanning sets for corresponding vectors, is singular. 4) >> A=[2 -14;1-12;-22-4]; >> rref(A) ans =R3?1, because the matrix A, which is formed by the 1-12000000 Or >> rank(A) ans =1 They are not spanning sets for 2. 1)R3?1. >> x1=[ -1;2; 3]; x2=[3 ;4; 2]; x=[2 ;6; 6]; y=[ -9 ;-2; 5]; >> A1=[x1,x2,x] ; >> rref(A1) ans =100010001x? Span(x1 , x2), for the vectors x1, x2, x are independent. Or >> rank(A1) ans =3 >> rank([x1, x2]) ans =2x? Span(x1 , x2), for the rank of{ x1, x2} is not equal to that of {x1, x2, x}. 2) >> rref([x1,x2,y]) ans =10301-2000 Result implies that y? Span(x1 , x2). 3. 1) >> x1=[1 ;0; 0]; x2=[0 ;0; 1]; x3=[