用Matlab学习线性代数 - 线性方程组与矩阵代数概要(9)

1 0 4 0 0 0 0 1 3 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 >> Z=[-4,-3,1,0,0,0]'; >> A*Z ans = 0 0 0 0 0 0 >> （6）

>> A=floor(20*rand(6));A(:,3)=A(:,1:2)*[4 3]'; >> y=floor(20*rand(6,1))-10; >> c=A*y; >> U=rref([A c]);

>> U(:,7)=zeros(6,1) U =

1 0 4 0 0 0 0 0 1 3 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 >> U=rref([A c]) U =

1 0 4 0 0 1 3 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 >> z=[-4,-3,1,0,0,0]'; >> w=[-23,-22,0,4,9,6]'; >> v=w+3*z； >> A*v-c ans =

0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 -23 -22 4 9 6 0 0 0 0 0 0 0 >> 第六题 ： （1）

A=[0,1,0,1,0,0,0,1;1,0,1,0,0,0,1,0;0,1,0,1,0,0,0,0;1,0,1,0,1,0,0,0;0,0,0,1,0,1,0,0;0,0,0,0,1,0,1,0;0,1,0,0,0,1,0,1;1,0,0,0,0,0,1,0] A =

0 1 0 1 0 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 1 0

（2） >> A^2 ans =

3 0 0 3 2 0 0 2 1 0 0 1 2 0 0 2 >> A1=A^2+A A1 =

3 1 1 3 2 1 1 2 1 0 0 1 2 0 0 2 2 0 0 3 1 0 0 1 1 0 0 1 2 1 1 2 2 1 1 3 1 1 0 1 1 0 0 1 1 0 0 1 2 0 0 2 1 0 0 1 1 0 0 1 1 0 1 1 2 1 1 2 2 0 0 2 1 0 0 1 1 0 0 1 3 0 0 2 2 1 1 2 1 0 0 1 1 0 1 1

2 1 1 0 1 1 3 1 1 2 0 1 0 1 1 2 sum(sum(A1(1:8,1:8))) ans = 72 (3)

>> A2=A^4+A A2 =

18 1 13 1 1 18 1 15 13 1 10 1 1 15 1 15 9 0 7 1 0 9 0 8 15 1 10 0 1 13 0 10 >> sum(sum(A2(1:8,1:8))) ans = 368

9 0 0 9 7 0 1 8 7 1 1 7 8 1 0 7 1 1 13 0 0 10 8 0 1 7 1 1 10 15 10 15