Solution6.3线性代数英文版第八版答案

线性代数英文单词

线性代数英语词汇大集合 ========================================================================= A adjont(adjugate) of matrix A A 的伴随矩阵 augmented matrix A 的增广矩阵 B block diagonal matrix 块对角矩阵 block matrix 块矩阵 basic solution set 基础解系 C Cauchy-Schwarz inequality 柯西 - 许瓦兹不等式 characteristic equation 特征方程 characteristic polynomial 特征多项式 coffcient matrix 系数矩阵 cofactor 代数余子式 cofactor expansion 代数余子式展开 column vector 列向量 commuting matrices 交换矩阵 consistent linear system 相容线性方程组 Cramer's rule 克莱姆法则 Cross- product term 交叉项 D Determinant 行列式 Diagonal entries 对角元素 Diagonal matrix 对角矩阵 Dimension of a vector space V 向量空间 V 的维数 E echelon matrix 梯形矩阵 eigenspace 特征空间 eigenvalue 特征值 eigenvector 特征向量

eigenvector basis 特征向量的基 elementary matrix 初等矩阵 elementary row operations 行初等变换 F full rank 满秩 fundermental set of solution 基础解系 G grneral solution 通解 Gram-Schmidt process 施密特正交化过程 H homogeneous linear equations 齐次线性方程组I identity matrix 单位矩阵 inconsistent linear system 不相容线性方程组indefinite matrix 不定矩阵 indefinit quatratic form 不定二次型 infinite-dimensional space 无限维空间 inner product 内积 inverse of matrix A 逆矩阵 J K L linear combination 线性组合 linearly dependent 线性相关 linearly independent 线性无关 linear transformation 线性变换 lower triangular matrix 下三角形矩阵 M main diagonal of matrix A 矩阵的主对角matrix 矩阵

同济大学线性代数第六版答案(全)

第一章 行列式 1. 利用对角线法则计算下列三阶行列式: (1)3811411 02---; 解 3 811411 02--- =2?(-4)?3+0?(-1)?(-1)+1?1?8 -0?1?3-2?(-1)?8-1?(-4)?(-1) =-24+8+16-4=-4. (2)b a c a c b c b a ; 解 b a c a c b c b a =acb +bac +cba -bbb -aaa -ccc =3abc -a 3-b 3-c 3. (3)2221 11c b a c b a ; 解 2 221 11c b a c b a =bc 2+ca 2+ab 2-ac 2-ba 2-cb 2 =(a -b )(b -c )(c -a ).

(4)y x y x x y x y y x y x +++. 解 y x y x x y x y y x y x +++ =x (x +y )y +yx (x +y )+(x +y )yx -y 3-(x +y )3-x 3 =3xy (x +y )-y 3-3x 2 y -x 3-y 3-x 3 =-2(x 3+y 3). 2. 按自然数从小到大为标准次序, 求下列各排列的逆序数: (1)1 2 3 4; 解 逆序数为0 (2)4 1 3 2; 解 逆序数为4: 41, 43, 42, 32. (3)3 4 2 1; 解 逆序数为5: 3 2, 3 1, 4 2, 4 1, 2 1. (4)2 4 1 3; 解 逆序数为3: 2 1, 4 1, 4 3. (5)1 3 ? ? ? (2n -1) 2 4 ? ? ? (2n ); 解 逆序数为2) 1(-n n : 3 2 (1个) 5 2, 5 4(2个) 7 2, 7 4, 7 6(3个)

线性代数introduction to vectors

An introduction to vectors Definition of a vector A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction. The direction of the vector is from its tail to its head. Two vectors are the same if they have the same magnitude and direction. This means that if we take a vector and translate it to a new position (without rotating it), then the vector we obtain at the end of this process is the same vector we had in the beginning. Two examples of vectors are those that represent force and velocity. Both force and velocity are in a particular direction. The magnitude of the vector would indicate the strength of the force or the speed associated with the velocity. We denote vectors using boldface as in a or b. Especially when writing by hand where one cannot easily write in boldface, people will sometimes denote vectors using arrows as in a or b, or they use other markings. We won't need to use arrows here. We denote the magnitude of the vector a by ∥a∥. When we want to refer to a number and stress that it is not a vector, we can call the number a scalar. We will denote scalars with italics, as in a or b . You can explore the concept of the magnitude and direction of a vector using the below applet. Note that moving the vector around doesn't change the vector, as the position of the vector doesn't affect the magnitude or the direction. But if you stretch or turn the vector by moving just its head or its tail, the magnitude or direction will change. (This applet also shows the coordinates of the vector, which you can read about in another page.) The magnitude and direction of a vector. The blue arrow represents a vector a . The two defining properties of a vector, magnitude and direction, are illustrated by a red bar and a green arrow, respectively. The length of the red bar is the magnitude ∥a∥ of the vector a. The green arrow always has length one, but its direction is the direction of the vector a.

线性代数 英文讲义

Chapter 1 Matrices and Systems of Equations Linear systems arise in applications to such areas as engineering, physics, electronics, business, economics, sociology（社会学）, ecology （生态学）, demography(人口统计学), and genetics（遗传学）, etc. §1. Systems of Linear Equations New words and phrases in this section: Linear equation 线性方程 Linear system，System of linear equations 线性方程组 Unknown 未知量 Consistent 相容的 Consistence 相容性 Inconsistent不相容的 Inconsistence 不相容性 Solution 解 Solution set 解集 Equivalent 等价的 Equivalence 等价性 Equivalent system 等价方程组 Strict triangular system 严格上三角方程组 Strict triangular form 严格上三角形式 Back Substitution 回代法 Matrix 矩阵 Coefficient matrix 系数矩阵 Augmented matrix 增广矩阵 Pivot element 主元 Pivotal row 主行 Echelon form 阶梯形 1.1 Definitions A linear equation (线性方程) in n unknowns（未知量）is 1122... n n a x a x a x b +++=

同济大学线性代数第五版课后习题答案

第一章 行列式 1 利用对角线法则计算下列三阶行列式 (1)3811 411 02--- 解 3 811411 02--- 2(4)30(1)(1)118 0 132(1)8 1( 4) (1) 248164 4 (2)b a c a c b c b a 解 b a c a c b c b a acb bac cba bbb aaa ccc 3abc a 3b 3c 3 (3)2 221 11c b a c b a

解 2 221 11c b a c b a bc 2ca 2ab 2ac 2ba 2cb 2 (a b )(b c )(c a ) (4)y x y x x y x y y x y x +++ 解 y x y x x y x y y x y x +++ x (x y )y yx (x y )(x y )yx y 3(x y )3x 3 3xy (x y )y 33x 2 y x 3y 3x 3 2(x 3 y 3) 2 按自然数从小到大为标准次序 求下列各排列的逆 序数 (1)1 2 3 4 解 逆序数为0 (2)4 1 3 2 解 逆序数为4 41 43 42 32 (3)3 4 2 1

解逆序数为5 3 2 3 1 4 2 4 1, 2 1 (4)2 4 1 3 解逆序数为3 2 1 4 1 4 3 (5)1 3 (2n1) 2 4 (2n) 解逆序数为 2)1 ( n n 3 2 (1个) 5 2 5 4(2个) 7 2 7 4 7 6(3个) (2n1)2(2n1)4(2n1)6 (2n1)(2n2) (n1个) (6)1 3 (2n1) (2n) (2n2) 2 解逆序数为n(n1) 3 2(1个) 5 2 5 4 (2个) (2n1)2(2n1)4(2n1)6

同济大学线性代数第五版课后习题答案

1 利用对角线法则计算下列三阶行列式 (1)3811 411 02--- 解 3 811411 02--- 2(4)30(1)(1)118 0 132(1)8 1( 4) (1) 248164 4 (2)b a c a c b c b a 解 b a c a c b c b a acb bac cba bbb aaa ccc 3abc a 3b 3c 3 (3)2221 11c b a c b a 解 2 221 11c b a c b a

bc 2ca 2ab 2ac 2ba 2cb 2 (a b )(b c )(c a ) (4)y x y x x y x y y x y x +++ 解 y x y x x y x y y x y x +++ x (x y )y yx (x y )(x y )yx y 3(x y )3x 3 3xy (x y )y 33x 2 y x 3y 3x 3 2(x 3 y 3) 2 按自然数从小到大为标准次序 求下列各排列的逆 序数 (1)1 2 3 4 解 逆序数为0 (2)4 1 3 2 解 逆序数为4 41 43 42 32 (3)3 4 2 1 解 逆序数为5 3 2 3 1 4 2 4 1, 2 1

(4)2 4 1 3 解逆序数为3 2 1 4 1 4 3 (5)1 3 (2n1) 2 4 (2n) 解逆序数为 2)1 ( n n 3 2 (1个) 5 2 5 4(2个) 7 2 7 4 7 6(3个) (2n1)2(2n1)4(2n1)6 (2n1)(2n2) (n1个) (6)1 3 (2n1) (2n) (2n2) 2 解逆序数为n(n1) 3 2(1个) 5 2 5 4 (2个) (2n1)2(2n1)4(2n1)6 (2n1)(2n2) (n1个)

(完整word版)《线性代数》英文专业词汇.docx

《线性代数》英文专业词汇 序号英文中文1Linear Algebra线性代数 2determinant行列式 3row行 4column列 5element元素 6diagonal对角线 7principal diagona主对角线 8auxiliary diagonal次对角线 9transposed determinant转置行列式 10triangular determinants三角行列式 11the number of inversions逆序数 12even permutation奇排列 13odd permutation偶排列 14parity奇偶性 15interchange互换 16absolute value绝对值 17identity恒等式 18n-order determinants n 阶行列式 19evaluation of determinant行列式的求值 20Laplace ’s expansion theorem拉普拉斯展开定理21cofactor余子式 22Algebra cofactor代数余子式 23the Vandermonde determinant范德蒙行列式 24bordered determinant加边行列式 25reduction of the order of a determinant降阶法 26method of Recursion relation递推法 27induction归纳法 28Cramer′s rule克莱姆法则 29matrix矩阵 30rectangular矩形的 31the zero matrix零矩阵

线性代数 英文讲义

Chapter 4 Linear Transformations In this chapter, we introduce the general concept of linear transformation from a vector space into a vector space. But, we mainly focus on linear transformations from n R to m R. §1 Definition and Examples New words and phrases Mapping 映射 Linear transformation 线性变换 Linear operator 线性算子 Dilation 扩张 Contraction 收缩 Projection 投影 Reflection 反射 Counterclockwise direction 反时针方向 Clockwise direction 顺时针方向 Image 像 Kernel 核 1.1 Definition ★Definition A mapping(映射) L: V W is a rule that produces a correspondence between two sets of elements such that to each element in the first set there corresponds one and only one element in the second set. ★Definition A mapping L from a vector space V into a vector space W is said to be a linear transformation（线性变换）if

同济大学线性代数第六版答案(全)

第一章行列式 1.利用对角线法则计算下列三阶行列式: (1)3 81141102---; 解3 81141102--- =2?(-4)?3+0?(-1)?(-1)+1?1?8 -0?1?3-2?(-1)?8-1?(-4)?(-1) =-24+8+16-4=-4. (2)b a c a c b c b a ; 解b a c a c b c b a =acb +bac +cba -bbb -aaa -ccc =3abc -a 3-b 3-c 3. (3)2 22111c b a c b a ; 解2 22111c b a c b a =bc 2+ca 2+ab 2-ac 2-ba 2-cb 2 =(a -b )(b -c )(c -a ). (4)y x y x x y x y y x y x +++.

解 y x y x x y x y y x y x +++ =x (x +y )y +yx (x +y )+(x +y )yx -y 3-(x +y )3-x 3 =3xy (x +y )-y 3-3x 2y -x 3-y 3-x 3 =-2(x 3+y 3). 2.按自然数从小到大为标准次序,求下列各排列的逆序数: (1)1 2 3 4; 解逆序数为0 (2)4 1 3 2; 解 逆序数为4: 41, 43, 42, 32. (3)3 4 2 1; 解 逆序数为5: 3 2, 3 1, 4 2, 4 1, 2 1. (4)2 4 1 3; 解 逆序数为3: 2 1, 4 1, 4 3. (5)1 3 ??? (2n -1) 2 4 ??? (2n ); 解 逆序数为2 )1(-n n : 3 2 (1个) 5 2, 5 4(2个) 7 2, 7 4, 7 6(3个) ?????? (2n -1)2, (2n -1)4, (2n -1)6,???, (2n -1)(2n -2)(n -1个) (6)1 3 ??? (2n -1) (2n ) (2n -2) ??? 2.

完整word版线性代数英文专业词汇x

《线性代数》英文专业词汇序号英文中文

1Linear Algebra线性代2determinant行列3row 4column5element元6diagonal对角7principal diagona主对角8auxiliary diagonal次对角9 transposed determinant转置行列10triangular determinants三角行列11the number of inversions逆序12even permutation奇排13odd permutation偶排14parity奇偶15interchange 互16absolute value绝对17identity恒等18 n-order determinants n 阶行列式 19evaluation of determinant行列式的求20 Laplace 's expansion theorem拉普拉斯展开21 cofactor余子22Algebra cofactor代数余子式23the Vandermonde determinant范德蒙行列24 bordered determinant加边行列25reduction of the order of a determinant降阶26method of Recursion relation递推27induction归纳28 Cramer′s rule克莱姆法29matrix矩30 rectangular矩形31the zero matrix零矩阵

32the identity matrix单位矩33symmetric对称的 序号英文中文 34skew-symmetric反对称35commutative law

工程数学线性代数第五版答案

线性代数重点 第一章 行列式 8. 计算下列各行列式(D k 为k 阶行列式): (1)a a D n 1 1???=, 其中对角线上元素都是a , 未写出的元素 都是0; 解 a a a a a D n 0 1 0 000 00 00 0 00 10 00? ????????????????????????????????=(按第n 行展开) ) 1()1(1 0 000 0 0 00 0 001 0 000)1(-?-+??????????????????????????????-=n n n a a a )1()1(2 )1(-?-????-+n n n a a a n n n n n a a a +? ??-?-=--+) 2)(2(1 )1()1(=a n -a n -2=a n -2(a 2-1). (2)x a a a x a a a x D n ????????????? ????????= ; 解 将第一行乘(-1)分别加到其余各行, 得

a x x a a x x a a x x a a a a x D n --??????????????????--???--???=000 0 00 0 , 再将各列都加到第一列上, 得 a x a x a x a a a a n x D n -??????????????????-???-???-+=0000 0 000 0 )1(=[x +(n -1)a ](x -a )n -1. (3)1 1 1 1 )( )1()( )1(1 1 11???-? ????????-? ?????-???--???-=---+n a a a n a a a n a a a D n n n n n n n ; 解 根据第6题结果, 有 n n n n n n n n n n a a a n a a a n a a a D )( )1()( )1( 11 11)1(1112)1(1-???--?????????-? ?????-???-???-=---++ 此行列式为范德蒙德行列式. ∏≥>≥++++--+--=1 12 )1(1)]1()1[()1(j i n n n n j a i a D ∏≥>≥++---=112 )1()]([)1(j i n n n j i ∏≥>≥++???+-++-? -?-=1 12 1 )1(2 )1()()1()1(j i n n n n n j i ∏≥>≥+-= 1 1)(j i n j i .

同济大学线性代数第六版答案(全)

同济大学线性代数第六版答案(全) 1 利用对角线法则计算下列三阶行列式201 (1)1 4 ***** 解1 4 183 2 ( 4) 3 0 ( 1) ( 1) 1 1 8 0 1 3 2 ( 1) 8 1 ( 4) ( 1) 2 4 8 16 4 4 abc (2)bca cababc 解bca cab acb bac cba bbb aaa ccc 3abc a3 b3 c3 111 (3)abc a2b2c2111 解abc a2b2c2 bc2 ca2 ab2 ac2 ba2 cb2 (a b)(b c)(c a) xyx y (4)yx yx x yxyxyx y 解yx yx x yxy x(x y)y yx(x y) (x y)yx y3 (x y)3 x3 3xy(x y) y3 3x2 y x3 y3 x3 2(x3 y3) 2 按自然数从小到大为标准次序求下列各排列的逆序数 (1)1 2 3 4 解逆序数为0 (2)4 1 3 2

解逆序数为4 41 43 42 32 (3)3 4 2 1 解逆序数为5 3 2 3 1 4 2 4 1, 2 1 (4)2 4 1 3 解逆序数为3 2 1 4 1 4 3 (5)1 3 (2n 1) 2 4 (2n) n(n 1) 解逆序数为 2 3 2 (1个) 5 2 5 4(2个) 7 2 7 4 7 6(3个) (2n 1)2 (2n 1)4 (2n 1)6 (2n 1)(2n 2) (n 1个) (6)1 3 (2n 1) (2n) (2n 2) 2 解逆序数为n(n 1) 3 2(1个) 5 2 5 4 (2个) (2n 1)2 (2n 1)4 (2n 1)6 (2n 1)(2n 2) (n 1个) 4 2(1个) 6 2 6 4(2个) (2n)2 (2n)4 (2n)6 (2n)(2n 2) (n 1个) 3 写出四阶行列式中含有因子a11a23的项解含因子a11a23的项的一般形式为 ( 1)ta11a23a3ra4s 其中rs是2和4构成的排列这种排列共有两个即24和42 所以含因子a11a23的项分别是 ( 1)ta11a23a32a44 ( 1)1a11a23a32a44 a11a23a32a44 ( 1)ta11a23a34a42 ( 1)2a11a23a34a42 a11a23a34a42 4 计算下列各行列式 41 (1)***-*****14 2 07 41 解***-*****c2 c***** 1 ***** 104 1 10 2 122 ( 1)4 3 *****c 4 7c***** 3 1 4 4 110c2 c***** 123 142c00 2 0 1 2c***** 2 (2)31 1***** 22 4 解31 ***** c 4 c3 223 1202r 4 r ***-*****06 ***-*****

线性代数英文词汇

英汉词汇（按英文字母排序） A adjont(adjugate) of matrix A A 的伴随矩阵 augmented matrix A 的增广矩阵 B block diagonal matrix 块对角矩阵 block matrix 块矩阵 basic solution set 基础解系

C Cauchy-Schwarz inequality 柯西 - 许瓦兹不等式characteristic equation 特征方程 characteristic polynomial 特征多项式 coffcient matrix 系数矩阵 cofactor 代数余子式 cofactor expansion 代数余子式展开 column vector 列向量 commuting matrices 交换矩阵 consistent linear system 相容线性方程组 Cramer's rule 克莱姆法则 Cross- product term 交叉项 D Determinant 行列式 Diagonal entries 对角元素 Diagonal matrix 对角矩阵 Dimension of a vector space V 向量空间V 的维数E echelon matrix 梯形矩阵 eigenspace 特征空间 eigenvalue 特征值 eigenvector 特征向量 eigenvector basis 特征向量的基 elementary matrix 初等矩阵

elementary row operations 行初等变换 F full rank 满秩 fundermental set of solution 基础解系 G grneral solution 通解 Gram-Schmidt process 施密特正交化过程 H homogeneous linear equations 齐次线性方程组I identity matrix 单位矩阵 inconsistent linear system 不相容线性方程组indefinite matrix 不定矩阵 indefinit quatratic form 不定二次型 infinite-dimensional space 无限维空间 inner product 内积

2017~2018 Final Exam 线性代数英文试题

Student Number: Your Name: 2016—2017 Fall Semester UNIVERSITY OF SCIENCE ＆ TECHNOLOGY BEIJING Linear Algebra Final Exam Time:09:00-11:30 A.M.Full Mark:100 Your Mark: Notation: Please fill out and sign the front of your exam booklet. No books or electronic devices allowed. No using any notes or formulas! No cheating! You may keep this paper. Solutions will be posted on the course website after the exam. Please do not answer the following problem until we give the signal. 1. (20 points) Let A =2 2 1 6 6 3 ?3 1 10 4 13 10 4 Find bases of the following vector spaces and statetheir dimensions. (a) The column space of A. (b) The row space of A. (c) The null space of A. (d) The orthogonal complement of the column space of A. 2. (15 points)Let A = 4?1 30 (a) Compute A k for all integers k≥0. Write the answer as explicitly as you can, in the form ofa 2×2-matrix with entries depending on k. (b) Solve the initial value problem x'(t) = A x(t) with x(0) =1 0 3. (10 points) (a) Let P n be the vector space of polynomials of degree less than or equal to n.Let T be the linear transformation from P3to P4defined by T(p)(t)=p(2) + (t– 2)p (t)+ t3p (5t) (You are not required to show that T is linear.) Find the matrix of T with respect to the B 3= {1, t, t2, t3} of P3 and the B 4 = {1,t,t2,t3,t4} of.P4 (b) Find the equation y = ax + b of the least-squares line that best fits the data points (1,2), (2,2), and (3,4).

线性代数课程专业词汇表

线性代数课程专业词汇表 英文单词或词组中文翻译书中出现页码 Linear equation 线性方程 1 Linear system(s) 线性方程组 1 Consistent 有解 2 Inconsistent 无解 2 Solution set of linear system 线性方程组的解集合 2 Equivalent systems 等价的线性方程组 3 Row operations 行变换 5 Strict triangular form 严格三角形式 5 Back substitution 回代法 6 Equivalent systems 等价的线性方程组 6 Coefficient matrix 系数矩阵 7 Coefficient matrix 系数矩阵 7 Augmented matrix 增广矩阵 8 Pivot 主元 8 Free variables 自由未知量 14 Lead variables 前变量 14 Gaussian elimination 高斯消元法 15 Overdetermined linear system 方程个数超过未知数个数的方程组 15 Row echelon form 行阶梯形 15 Underdetermined linear system 方程个数低于未知数个数的方程组 17 Gauss-Jordan reduction 高斯-若当归纳法 18 Reduced row echelon form 减少的行阶梯形 18 Homogeneous linear system 齐次线性方程组 22 Homogeneous system 齐次线性方程组 22 nontrivial solution 非零解 22 Trivial solution 平凡解，全零解 22 Matrix algebra 矩阵代数 30 Scalars 常数 30 Column vector(s) 列向量 31 Euclidean n-space 欧几里得空间 31 Row vector(s) 行向量 31 Vector(s）向量 31 Addition of matrices 矩阵加法 32 Addition of matrices 矩阵加法 32 Equality of matrices 矩阵相等 32 Scalar multiplication for matrices 矩阵的数乘 32 Scalar multiplication of matrices 矩阵的数乘 32 Zero matrix 零矩阵 33 Scalar product 内积 34 Linear combination 线性组合 36 Consistency Theorem 解的存在性定理 37 Multiplication of matrices 矩阵乘法 38

同济大学线性代数第六版答案(全)

同济大学线性代数第六版答案(全) 第一章 行列式 1. 利用对角线法则计算下列三阶行列式: (1)3 811411 02---; 解 3 811411 02--- =2?(-4)?3+0?(-1)?(-1)+1?1?8 -0?1?3-2?(-1)?8-1?(-4)?(-1) =-24+8+16-4=-4. (2)b a c a c b c b a ; 解 b a c a c b c b a =acb +bac +cba -bbb -aaa -ccc =3abc -a 3-b 3-c 3. (3)2221 11c b a c b a ; 解 2 221 11c b a c b a

=bc 2+ca 2+ab 2-ac 2-ba 2-cb 2 =(a -b)(b -c)(c -a). (4)y x y x x y x y y x y x +++. 解 y x y x x y x y y x y x +++ =x(x +y)y +yx(x +y)+(x +y)yx -y 3-(x +y)3-x 3 =3xy(x +y)-y 3-3x 2 y -x 3-y 3-x 3 =-2(x 3+y 3). 2. 按自然数从小到大为标准次序, 求下列各排列的逆序数: (1)1 2 3 4; 解 逆序数为0 (2)4 1 3 2; 解 逆序数为4: 41, 43, 42, 32. (3)3 4 2 1; 解 逆序数为5: 3 2, 3 1, 4 2, 4 1, 2 1. (4)2 4 1 3; 解 逆序数为3: 2 1, 4 1, 4 3.

(5)1 3 ??? (2n-1) 2 4 ??? (2n); 解逆序数为 2)1 (- n n: 3 2 (1个) 5 2, 5 4(2个) 7 2, 7 4, 7 6(3个) ?????? (2n-1)2,(2n-1)4,(2n-1)6,???,(2n-1)(2n-2) (n-1个) (6)1 3 ???(2n-1) (2n) (2n-2) ??? 2. 解逆序数为n(n-1) : 3 2(1个) 5 2, 5 4 (2个) ?????? (2n-1)2,(2n-1)4,(2n-1)6,???,(2n-1)(2n-2) (n-1个) 4 2(1个) 6 2, 6 4(2个) ?????? (2n)2, (2n)4, (2n)6,???, (2n)(2n-2) (n-1个)

同济大学工程数学线性代数第六版答案全

第一章行列式 1?利用对角线法则计算下列三阶行列式? (1)381141102---? 解3 81141102--- ?2?(?4)?3?0?(?1)?(?1)?1?1?8 ?0?1?3?2?(?1)?8?1?(?4)?(?1) ??24?8?16?4??4? (2)b a c a c b c b a ? 解b a c a c b c b a ?acb ?bac ?cba ?bbb ?aaa ?ccc ?3abc ?a 3?b 3?c 3? (3)222111c b a c b a ? 解2 22111c b a c b a ?bc 2?ca 2?ab 2?ac 2?ba 2?cb 2 ?(a ?b )(b ?c )(c ?a )?

(4)y x y x x y x y y x y x +++? 解y x y x x y x y y x y x +++ ?x (x ?y )y ?yx (x ?y )?(x ?y )yx ?y 3?(x ?y )3?x 3 ?3xy (x ?y )?y 3?3x 2y ?x 3?y 3?x 3 ??2(x 3?y 3)? 2?按自然数从小到大为标准次序?求下列各排列的逆序数? (1)1234? 解逆序数为0 (2)4132? 解逆序数为4?41?43?42?32? (3)3421? 解逆序数为5?32?31?42?41,21? (4)2413? 解逆序数为3?21?41?43? (5)13???(2n ?1)24???(2n )? 解逆序数为2 ) 1(-n n ? 32(1个) 52?54(2个) 72?74?76(3个) ?????? (2n ?1)2?(2n ?1)4?(2n ?1)6?????(2n ?1)(2n ?2)(n ?1个) (6)13???(2n ?1)(2n )(2n ?2)???2? 解逆序数为n (n ?1)? 32(1个) 52?54(2个) ?????? (2n ?1)2?(2n ?1)4?(2n ?1)6?????(2n ?1)(2n ?2)(n ?1个) 42(1个) 62?64(2个) ??????

线性代数同济大学第五版课后习题答案

线性代数同济大学第五版课后习题答案 第五版线性代数同济版答案第一章行列式 1用对角法则计算下列三阶行列式 (1) 2011年？4？1？183 解决办法 2011年？4？1？183 2(4)3 0(1)(1)1 1 8 0 1 3 2(1)8 1(4)(1)24 8 16 4 4 (2) abcbcacab 解决办法 abcbcacab acb bac cba bbb aaa ccc 3abc a3 b3 c3 111abc222abc (3) 111abc222abc解决方案 bc2 ca2 ab2 ac2 ba2 cb2 (a)b)c)c)a) xyx？yyx？yxx？yxy (4) 解决办法 x(x y)y yx(x y)(x y)yx y3(x y)3 x3 3xy(x y)y3 x2 y x3 y3 x32(x3 y3) 根据自然数从小到大的标准顺序，找出下列排列的逆序数xyx？yyx？

yxx？yxy (1)1 2 3 4解的逆序数是0 (2)4 1 3 2 反向订单号是4 41 43 42 32 (3)3 4 2 1 逆解的数目是5 3 2 3 1 4 2 4 1，2 1 (4)2 4 1 3 逆解的个数是3 2 1 4 1 4 3 (5)1 3 (2n 1) 2 4 (2n) n(n )?1)解的逆序数为 2 3 2 (1) 5 2 5 4(2) 7 2 7 4 7 6(3) (2n 1)2 (2n 1)4 (2n 1)6 (2n 1)(2n 2) (n (6)13(2 n1)(2n)(2 N2)2解的逆序数是n(n 1) 3 2(1) 5 2 5 4 (2) (2 n1)2(2 n1)4(2 n1)6(2 n1)(2 N2)(n42(1) 6 2 6 4(2) (2n)2 (2n)4 (2n)6 (2n)(2n 2) (n 1) 3将包含因子a11a23的项写入四阶行列式以求解包含因子a11a23的项的一般形式是(1)ta11a23a3ra4s 当rs是2和4的排列时，有两个这样的排列，即24和42，因此包含因子a11a23的项分别是 (1)ta 11a 23 a 32 a 44(1)1a 11 a 23 a 32 a 44 a 11 a 23 a 32 a 44)11 (1)ta 11 a 23 a 34 a 42(1)2 a 11 a 23 a 34 a 42 a 11 a 23 a 34 a 42 4计算下列行列式