第一课作业
2.2
（1）
> A=matrix(1:20,4,5)
> A
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    5    9   13   17
[2,]    2    6   10   14   18
[3,]    3    7   11   15   19
[4,]    4    8   12   16   20
> B=matrix(1:20,nrow=4,ncol=5,byrow=T)
> B
     [,1] [,2] [,3] [,4] [,5]
[1,]    1    2    3    4    5
[2,]    6    7    8    9   10
[3,]   11   12   13   14   15
[4,]   16   17   18   19   20
> C=A+B
> C
     [,1] [,2] [,3] [,4] [,5]
[1,]    2    7   12   17   22
[2,]    8   13   18   23   28
[3,]   14   19   24   29   34
[4,]   20   25   30   35   40

（2）
> D=A%*%t(B)
> D
[,1] [,2] [,3] [,4]
[1,] 175 400 625 850
[2,] 190 440 690 940
[3,] 205 480 755 1030
[4,] 220 520 820 1120

（3）

> E=A*B
> E
     [,1] [,2] [,3] [,4] [,5]
[1,]    1   10   27   52   85
[2,]   12   42   80 126 180
[3,]   33   84 143 210 285
[4,]   64 136 216 304 400

（4）
> F=A[1:3,1:3]
> F
     [,1] [,2] [,3]
[1,]    1    5    9
[2,]    2    6   10
[3,]    3    7   11
（5）
> G=B[1:4,-3]
> G
     [,1] [,2] [,3] [,4]
[1,]    1    2    4    5
[2,]    6    7    9   10
[3,]   11   12   14   15
[4,]   16   17   19   20
> G=B[,c(1,2,4,5)]
> G
     [,1] [,2] [,3] [,4]
[1,]    1    2    4    5
[2,]    6    7    9   10
[3,]   11   12   14   15
[4,]   16   17   19   20

2.3
> x=c(rep(1,5),rep(2,3),rep(3,4),rep(4,2));
> x
[1] 1 1 1 1 1 2 2 2 3 3 3 3 4 4
> is.vector(x)
[1] TRUE

2.4

> n=5
> H=array(0,dim=c(n,n))
> H
     [,1] [,2] [,3] [,4] [,5]
[1,]    0    0    0    0    0
[2,]    0    0    0    0    0
[3,]    0    0    0    0    0
[4,]    0    0    0    0    0
[5,]    0    0    0    0    0
> for (i in 1:n){for (j in 1:n){H[i,j]<-1/(i+j-1)}}
> H
          [,1]      [,2]      [,3]      [,4]      [,5]
[1,] 1.0000000 0.5000000 0.3333333 0.2500000 0.2000000
[2,] 0.5000000 0.3333333 0.2500000 0.2000000 0.1666667
[3,] 0.3333333 0.2500000 0.2000000 0.1666667 0.1428571
[4,] 0.2500000 0.2000000 0.1666667 0.1428571 0.1250000
[5,] 0.2000000 0.1666667 0.1428571 0.1250000 0.1111111

(1)
> det(H)
[1] 3.749295e-12

(2)
> solve(H)
      [,1]   [,2]    [,3]    [,4]   [,5]
[1,]    25   -300    1050   -1400    630
[2,] -300   4800 -18900   26880 -12600
[3,] 1050 -18900   79380 -117600 56700
[4,] -1400 26880 -117600 179200 -88200
[5,]   630 -12600   56700 -88200 44100
> H%*%solve(H)
              [,1]         [,2]          [,3]         [,4]          [,5]
[1,] 1.000000e+00 4.058975e-13 -9.769963e-14 4.760636e-13 -2.057021e-12
[2,] -1.089406e-15 1.000000e+00 -1.737277e-12 2.635225e-12 -2.529976e-12
[3,] 3.122502e-15 1.648681e-13 1.000000e+00 1.219469e-12 4.298784e-13
[4,] -1.421085e-14 2.273737e-13 9.094947e-13 1.000000e+00 -9.094947e-13
[5,] -5.467848e-15 2.545741e-13 6.608047e-13 1.150191e-12 1.000000e+00

(3)
> eigen(H)
$values
[1] 1.567051e+00 2.085342e-01 1.140749e-02 3.058980e-04 3.287929e-06

$vectors
[,1] [,2] [,3] [,4] [,5]
[1,] 0.7678547 0.6018715 -0.2142136 0.04716181 0.006173863
[2,] 0.4457911 -0.2759134 0.7241021 -0.43266733 -0.116692747
[3,] 0.3215783 -0.4248766 0.1204533 0.66735044 0.506163658
[4,] 0.2534389 -0.4439030 -0.3095740 0.23302452 -0.767191193
[5,] 0.2098226 -0.4290134 -0.5651934 -0.55759995 0.376245545

2.5
> seq=1:5
> name=c("张三","李四","王五","赵六","丁一")
> sex=c("女","男","女","男","女")
> sex
[1] "女" "男" "女" "男" "女"
> age=c(14,15,16,14,15)
> age
[1] 14 15 16 14 15
> weight=c(42.0,49.0,41.5,52.0,45.5)
> heigh=c(156,165,157,162,159)
> student=data.frame('序号'=seq,'姓名'=name,'性别'=sex,'身高/cm'=heigh,'体重/kg'=weight)
> student
序号姓名性别身高.cm 体重.kg
1    1 张三   女     156    42.0
2    2 李四   男     165    49.0
3    3 王五   女     157    41.5
4    4 赵六   男     162    52.0
5    5 丁一   女     159    45.5

2.6
> student=read.table("student.txt")
> student
    V1   V2   V3      V4      V5
1 序号姓名性别身高.cm 体重.kg
2    1 张三   女     156    42.0
3    2 李四   男     165    49.0
4    3 王五   女     157    41.5
5    4 赵六   男     162    52.0
6    5 丁一   女     159    45.5
> student=read.table("student.txt",header=F)
> student
    V1   V2   V3      V4      V5
1 序号姓名性别身高.cm 体重.kg
2    1 张三   女     156    42.0
3    2 李四   男     165    49.0
4    3 王五   女     157    41.5
5    4 赵六   男     162    52.0
6    5 丁一   女     159    45.5
> student=read.table("student.txt",header=T)
> student
序号姓名性别身高.cm 体重.kg
1    1 张三   女     156    42.0
2    2 李四   男     165    49.0
3    3 王五   女     157    41.5
4    4 赵六   男     162    52.0
5    5 丁一   女     159    45.5

> write.csv(student,file="student.csv")

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第一课作业

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