江西科技师范大学实验报告课程数学建模系别数学与计算机科学学院班级11数学与应用数学学号姓名报告规格一、实验目的二、实验原理三、实验仪器四、实验方法及步骤五、实验记录及数据处理六、误差分析及问题讨论实验一利用矩阵的运算方法求方程组的解。A=[2,1,3;-1,2,5;4,-1,2];b=[2;3;5];c=[Ab];[rank(A),rank(c)]ans=33因此，此方程组有唯一解x=inv(A)*bx=-0.1053-2.36841.52632.求上述线性方程组系数矩阵A的秩、特征值和特征向量秩A=[2,1,3;-1,2,5;4,-1,2];rank(A)ans=3特征值和特征向量A=[2,1,3;-1,2,5;4,-1,2];eig(A)ans=5.53610.2319+1.8380i0.2319-1.8380i>>[v,d]=eig(A)v=0.6162-0.2098+0.2415i-0.2098-0.2415i0.5796-0.8683-0.86830.53320.2651-0.2709i0.2651+0.2709id=5.53610000.2319+1.8380i0000.2319-1.8380i即，特征值X1=5.5361，X2=0.2319+1.8380i，X3=0.2319-1.8380i，其对应的特征向量为X10.6162X2-0.2098+0.2415iX3-0.2098-0.2415i0.5796-0.8683-0.86830.53320.2651-0.2709i0.2651+0.2709i3.在同一坐标面上绘制出的图形，要求：线型和颜色区分，并且在图的右上角用图例标出；注明横纵为时间，纵轴为幅值。x=0:pi/1800:2*pi;plot(x,sin(x),x,cos(x));实验二1.用matlab求解线性规划问题：约束条件为：c=[3;2;-8;5];A=[-36-52;7-3-13];b=[-3;-1];aeq=[181-1];beq=-2;vlb=[0;-inf;0;-inf];[x,fval]=linprog(c,A,b,aeq,beq,vlb)x=1.0e+008*0.0414-0.72135.3595-0.3694fval=-4.6042e+009c=[3,2,-8,5];A=[7,-3,-1,3;3,-6,5,-2]b=[-1;-3]aeq=[1,8,1,-1]beq=[-2]vlb=[0,-inf,0,-inf][x,fval]=linprog(c,A,b,aeq,beq,vlb)A=7-3-133-65-2b=-1-3aeq=181-1beq=-2vlb=0-Inf0-InfExiting:Oneormoreoftheresiduals,dualitygap,ortotalrelativeerrorhasstalled:theprimalappearstobeinfeasible(andthedualunbounded).(Thedualresidual<TolFun=1.00e-008.)x=0.00000.45830.00000.1250fval=1.5417实验三1.求微分方程的解。dsolve('Dy+2*x*y=x*exp(-x*x)')ans=(1/2*exp(-x*(x-2*t))+C1)*exp(-2*x*t)求微分方程在满足条件下的特解，并画出解函数的图形。[x,y]=dsolve('Dx+5*x+y=exp(t)','Dy-x-3*y=0','x(0)=1','y(0)=0','t')x=-4*exp((-1+15^(1/2))*t)*(13/330*15^(1/2)+1/22)+exp((-1+15^(1/2))*t)*(13/330*15^(1/2)+1/22)*15^(1/2)-4*exp(-(1+15^(1/2))*t)*(-13/330*15^(1/2)+1/22)-exp(-(1+15^(1/2))*t)*(-13/330*15^(1/2)+1/22)*15^(1/2)+2/11*exp(t)y=exp((-1+15^(1/2))*t)*(13/330*15^(1/2)+1/22)+exp(-(1+15^