I have a matrix in R as follows:

```
dat <- matrix(c(2,3,5,7,8,4), ncol = 6)
colnames(dat) <- c("A(1,1)", "A(1,2)", "A(1,3)", "A(2,2)", "A(2,3)", "A(3,3)")
```

How can I create a square symmetric matrix based on an `apply`

function that has the following form:

```
A(1,1) A(1,2) A(1,3)
A(2,1) A(2,2) A(2,3)
A(3,1) A(3,2) A(3,3)
```

Note that `A(1,2)=A(2,1)`

### >Solution :

This isn’t based on `apply`

but it shows how you can use `lower.tri`

and `upper.tri`

to create a symmetric matrix given a vector of elements. It shows the 3×3 case, but will easily generalize to larger `n`

:

```
dat <- matrix(rep(0,9),nrow = 3)
dat[lower.tri(dat,diag = TRUE)] <- c(2,3,5,7,8,4)
dat[upper.tri(dat)] <- t(dat)[upper.tri(dat)]
print(dat)
```

Result:

```
[,1] [,2] [,3]
[1,] 2 3 5
[2,] 3 7 8
[3,] 5 8 4
```