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How to generate a matrix of difference of two vectors in R

I have two vectors and I want to get a matrix of differences:

a = 1:4
b = 1:4

     [,1] [,2] [,3] [,4]
[1,]    0    1    2    3
[2,]   -1    0    1    2
[3,]   -2   -1    0    1
[4,]   -3   -2   -1    0

How can this be done? Thanks!

-outer(1:4, 1:4, '-')
##      [,1] [,2] [,3] [,4]
## [1,]    0    1    2    3
## [2,]   -1    0    1    2
## [3,]   -2   -1    0    1
## [4,]   -3   -2   -1    0

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