How to multiply a matrix with a vector in R?

R ProgrammingServer Side ProgrammingProgramming

When we multiply a matrix with a vector the output is a vector. Suppose we have a matrix M and vector V then they can be multiplied as M%*%V. To understand the step-by-step multiplication, we can multiply each value in the vector with the row values in matrix and find out the sum of that multiplication.

Example1

 Live Demo

M1<-matrix(1:25,nrow=5)
M1

Output

   [,1] [,2] [,3] [,4] [,5]
[1,] 1    6   11   16   21
[2,] 2    7   12   17   22
[3,] 3    8   13   18   23
[4,] 4    9   14   19   24
[5,] 5   10   15   20   25

Example

V1<-1:5
V1
[1] 1 2 3 4 5
M1%*%V1

Output

    [,1]
[1,] 215
[2,] 230
[3,] 245
[4,] 260
[5,] 275

Example2

 Live Demo

M2<-matrix(1:100,nrow=10)
M2

Output

    [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
[1,] 1   11    21    31   41   51   61   71   81   91
[2,] 2   12    22    32   42   52   62   72   82   92
[3,] 3   13    23    33   43   53   63   73   83   93
[4,] 4   14    24    34   44   54   64   74   84   94
[5,] 5   15    25    35   45   55   65   75   85   95
[6,] 6   16    26    36   46   56   66   76   86   96
[7,] 7   17    27    37   47   57   67   77   87   97
[8,] 8   18    28    38   48   58   68   78   88   98
[9,] 9   19    29    39   49   59   69   79   89   99
[10,] 10 20    30    40   50   60   70   80   90  100

Example

V2<-1:10
V2
[1] 1 2 3 4 5 6 7 8 9 10
M2%*%V2

Output

   [,1]
[1,] 3355
[2,] 3410
[3,] 3465
[4,] 3520
[5,] 3575
[6,] 3630
[7,] 3685
[8,] 3740
[9,] 3795
[10,] 3850

Example3

 Live Demo

M3<-matrix(rnorm(36,5,1),nrow=18)
M3

Output

       [,1]     [,2]
[1,] 3.627929 6.929146
[2,] 3.363237 4.400114
[3,] 4.640349 5.089977
[4,] 6.201115 5.483314
[5,] 4.354126 7.024478
[6,] 4.489391 6.631517
[7,] 4.400877 6.370375
[8,] 5.545603 2.586863
[9,] 4.508706 4.145658
[10,] 5.191536 5.562368
[11,] 4.441472 4.634800
[12,] 5.922700 4.657329
[13,] 6.153998 4.224459
[14,] 3.627590 4.987152
[15,] 6.290181 5.699693
[16,] 6.154902 5.031921
[17,] 6.445679 5.216649
[18,] 5.261013 5.407813

Example

V3<-c(5,10)
V3
[1] 5 10
M3%*%V3

Output

      [,1]
[1,] 87.43110
[2,] 60.81733
[3,] 74.10152
[4,] 85.83872
[5,] 92.01541
[6,] 88.76213
[7,] 85.70814
[8,] 53.59664
[9,] 64.00011
[10,] 81.58136
[11,] 68.55536
[12,] 76.18679
[13,] 73.01458
[14,] 68.00947
[15,] 88.44784
[16,] 81.09372
[17,] 84.39489
[18,] 80.38319

Example4

 Live Demo

M4<-matrix(rpois(50,10),ncol=5)
M4

Output

   [,1] [,2] [,3] [,4] [,5]
[1,] 12   2    9    4   14
[2,] 13  12   10    5   13
[3,] 10   8    9   12    9
[4,] 11   9    9   10   11
[5,] 12  11   14    6    8
[6,] 12   5   13    8   13
[7,] 16  11   10   14   10
[8,] 12  11   13   12    6
[9,] 4    7    5    8   10
[10,] 9  14   10   13   15

Example

V4<-1:5
V4
[1] 1 2 3 4 5
M4%*%V4

Output

   [,1]
[1,] 129
[2,] 152
[3,] 146
[4,] 151
[5,] 140
[6,] 158
[7,] 174
[8,] 151
[9,] 115
[10,] 194

Example

M5<-matrix(sample(0:9,20,replace=TRUE),ncol=5)
M5

Output

[,1] [,2] [,3] [,4] [,5]
[1,] 5 8 0 7 0
[2,] 9 9 7 8 0
[3,] 9 1 7 0 9
[4,] 6 6 5 7 6

Example

V5<-c(2,4,6,8,10)
V5
[1] 2 4 6 8 10
M5%*%V5

Output

    [,1]
[1,] 98
[2,] 160
[3,] 154
[4,] 182
raja
Published on 17-Oct-2020 17:39:47
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