专业 姓名 学号 成绩
52,0.0002 53,10000 54,0.0002 55,10000 56,0.0002 57,10000 58,0.0002 59,10000 60,0.0002 61,10000 62,0.0002 63,10000 64,0.0002 65,10000 66,0.0002 67,10000 68,0.0002 69,10000 70,0.0002 71,10000 72,0.0002 73,10000 74,0.0002 75,10000 76,0.0002 77,10000 78,0.0002 79,10000 80,0.0002 81,10000 82,0.0002 83,10000 84,0.0002 85,10000 86,0.0002 87,10000 88,0.0002 89,10000
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数学实验实验报告
专业 姓名 学号 成绩
90,0.0002 91,10000 92,0.0002 93,10000 94,0.0002 95,10000 96,0.0002 97,10000 98,0.0002 99,10000 100,0.0002
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数学实验实验报告
专业 姓名 学号 成绩
第三次练习
教学要求：理解线性映射的思想，会用线性映射和特征值的思想方法解决诸如天气等实际问题。 3.1 对A????42?(0)(0)TT，，求出{xn}的通项. (x,x)?(1,2)?12?13??程序：
A=sym('[4,2;1,3]'); [P,D]=eig(A) Q=inv(P) syms n; xn=P*(D.^n)*Q*[1;2] 结果： P =
[ 2, -1] [ 1, 1] D = [ 5, 0] [ 0, 2] Q =
[ 1/3, 1/3] [ -1/3, 2/3] xn =
2*5^n-2^n 5^n+2^n 3.2 B??0.40.2?1(0)(0)TT对于练习1中的，，(x,x)?(1,2)A???B12??10?0.10.3?求出{xn}的通项. 程序：
A=sym('[2/5,1/5;1/10,3/10]'); %没有sym下面的矩阵就会显示为小数 [P,D]=eig(A)
数学实验实验报告
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专业 姓名 学号 成绩
Q=inv(P)
xn=P*(D.^n)*Q*[1;2] 结果： P = [ 2, -1] [ 1, 1] D = [ 1/2, 0] [ 0, 1/5] Q =
[ 1/3, 1/3] [ -1/3, 2/3] xn =
2*(1/2)^n-(1/5)^n (1/2)^n+(1/5)^n
(n)x23.3 对随机给出的(x,x)，观察数列{(n)}.该数列有极限吗?
x1(0)1(0)T2>> A=[4,2;1,3]; a=[];
x=2*rand(2,1)-1; for i=1:20
a(i,1:2)=x;
x=A*x; end for i=1:20
if a(i,1)==0
else t=a(i,2)/a(i,1);
fprintf('%g,%g\\n',i,t); end
end
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专业 姓名 学号 成绩
(n)x2结论：在迭代18次后，发现数列{(n)}存在极限为0.5
x11,-0.597298 2,-0.282275 3,0.0445866 4,0.277259 5,0.402189 6,0.459283 7,0.483443 8,0.493333 9,0.497326 10,0.498929 11,0.499572 12,0.499829 13,0.499931 14,0.499973 15,0.499989 16,0.499996 17,0.499998 18,0.499999 19,0.5 20,0.5
3.4 对120页中的例子，继续计算xn,yn(n?1,2,?).观察{xn},{yn}及
m(xn)的极限是否存在. （120页练习9）
>> A=[2.1,3.4,-1.2,2.3;0.8,-0.3,4.1,2.8;2.3,7.9,-1.5,1.4;3.5,7.2,1.7,-9.0]; x0=[1;2;3;4]; x=A*x0; for i=1:1:100 a=max(x); b=min(x); m=a*(abs(a)>abs(b))+b*(abs(a)<=abs(b)); y=x/m; x=A*y; end
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