This tutorial explains how to multiply a matrix by a vector in R.

**Multiplying a Matrix by a Vector**

Consider the following code that generates a matrix and a vector in R:

#Create a vector of numbers 1, 2, 3 vector <- c(1:3) vector # [1] 1 2 3 #create a matrix with three columns and five rows matrix <- as.matrix(cbind(a = 1:5, b = 6:10, c= 11:15)) matrix # a b c # [1,] 1 6 11 # [2,] 2 7 12 # [3,] 3 8 13 # [4,] 4 9 14 # [5,] 5 10 15

Suppose we want to multiply the matrix by the vector such that we get a new matrix with the following values:

(1*1 + 6*2 + 11*3) = 46

(2*1 + 7*2 + 12*3) = 52

(3*1 + 8*2 + 13*3) = 58

(4*1 + 9*2 + 14*3) = 64

(5*1 + 10*2 + 15*3) = 70

To perform this type of element-wise multiplication in R, we can simply use the **%*%** operator:

#multiply the matrix by the vector matrix %*% vector # [,1] # [1,] 46 # [2,] 52 # [3,] 58 # [4,] 64 # [5,] 70

The end result is a 5×1 matrix.