MATLAB线性代数课后题.doc

第1章 行列式1. 计算行列式解：2 用克拉默法则解下列方程组 ： 解： 3 证明 证明：ans =(- a2*b + a2*c + a*b2 - a*c2 - b2*c + b*c2)*d4 + (a4*b - a4*c - a*b4 + a*c4 + b4*c - b*c4)*d2 + (- a4*b2 + a4*c2 + a2*b4 - a2*c4 - b4*c2 + b2*c4)*d + a4*b2*c - a4*b*c2 - a2*b4*c + a2*b*c4 + a*b4*c2 - a*b2*c4ans=a4*b2*c - a4*b2*d - a4*b*c2 + a4*b*d2 + a4*c2*d - a4*c*d2 - a2*b4*c + a2*b4*d + a2*b*c4 - a2*b*d4 - a2*c4*d + a2*c*d4 + a*b4*c2 - a*b4*d2 - a*b2*c4 + a*b2*d4 + a*c4*d2 - a*c2*d4 - b4*c2*d + b4*c*d2 + b2*c4*d - b2*c*d4 - b*c4*d2 + b*c2*d4左边等于右边所以可以得出证明。第2章 矩阵及其运算1. 计算下列乘积 解：2. 设 解：3. 求下列矩阵的逆矩阵： 解：（2） 解：第3章 矩阵的初等变换与线性方程组1. 解：2 求解下列齐次线性方程组 解：3 求解下列非齐次线性方程组解：第4章 向量组的线性相关性1. 求下列非齐次方程组的一个解及对应的齐次方程组的基础解系。 解：2. 求基础解系解： 3. 已知的两个基为： ，求由基a1,a2,a3到b1,b2,b3的过渡矩阵P.解： 第5章 相似矩阵及二次型1. 求下列矩阵的特征值与特征向量 (1) 解：（X的每个列向量都是特征向量，B的对角线是特征值）(2) 解：2. 设3阶方阵A的特征值为1=2,2=-2,3=1对应的特征向量依次为 解：令P=(p1, p2, p3), 则P-1AP=diag(2, -2, 1)=L, A=PLP-1.3. 设3阶对称矩阵A的特征值l1=6, l2=3, l3=3, 与特征值l1=6对应的特征向量为p1=(1, 1, 1)T, 求A.解: 设. 第6章 线性空间与线性变换1. 在R4中取两个基 e1=(1,0,0,0)T, e2=(0,1,0,0)T, e3=(0,0,1,0)T, e4=(0,0,0,1)T; a1=(2,1,-1,1)T, a2=(0,3,1,0)T, a3=(5,3,2,1)T, a3=(6,6,1,3)T. 求由前一个基到后一个基的过渡矩阵; 解：由题意知,2. 在R3中求向量a=(3, 7, 1)T在基a1=(1, 3, 5)T, a2=(6, 3, 2)T, a3=(3, 1, 0)T下的坐标.设e1, e2, e3是R3的自然基, 则 (a1, a2, a3)=(e1, e2, e3)A, (e1, e2, e3)=(a1, a2, a3)A-1,其中, . 因为 3. 在R3取两个基 a1=(1, 2, 1)T, a2=(2, 3, 3)T, a3=(3, 7, 1)T; b1=(3, 1, 4)T, b2=(5, 2, 1)T, b3=(1, 1, -6)T. 试求坐标变换公式. 设e1, e2, e3是R3的自然基, 则 (b1, b2, b1)=(e1, e2, e3)B, (e1, e2, e3)=(b1, b2, b1)B-1, (a1, a2, a1)=(e1, e2, e3)A=(b1, b2, b1)B-1A,其中 , . 设任意向量a在基a1, a2, a3下的坐标为(x1, x2, x3)T, 则,故a在基b1, b2, b3下的坐标为Acknowledgements My deepest gratitude goes first and foremost to Professor aaa , my supervisor, for her constant encouragement and guidance. She has walked me through all the stages of the writing of this thesis. Without her consistent and illuminating instruction, this thesis could not havereached its present form. Second, I would like to express my heartfelt gratitude to Professor aaa, who led me into the world of translation. I am also greatly indebted to the professors and teachers at the Department of English: Professor dddd, Professor ssss, who have instructed and helped me a lot in the past two years. Last my thanks would go to my beloved family for their loving considerations and great confidence in me all through these years. I also owe my sincere gratitude to my friends and my fellow classmates who gave me their help and time in listening to me and helping me work out my problems during the difficult course of the thesis. My deepest gratitude goes first and foremost to Professor aaa , my supervisor, for her constant encouragement and guidance. She has walked me through all the stages of the writing of this thesis. Without her consistent and illuminating instruction, this thesis could not havereached its present form. Second, I would like to express my heartfelt gratitude to Professor aaa, who led me into the world of translation. I am also greatly indebted to the professors and teachers at the Department of English: Professor dddd, Professor ssss, who have instructed and helped me a lot in the past two years. Last my thanks would go to my beloved family for their loving considerations and great confidence in me all through these years. I also owe my sincere gratitude to my friends and my fellow classmates who gave me their help and time in listening to me and helping me work out my problems during the difficult course of the thesis.