Solution 1
u <- 4
v <- 8
u + v## [1] 12u - v## [1] -4u * v## [1] 32u / v## [1] 0.5u^v## [1] 65536Solution 2
u <- c(4, 5, 6)
v <- c(1, 2, 3)
u + v## [1] 5 7 9u - v## [1] 3 3 3u * v## [1] 4 10 18u / v## [1] 4.0 2.5 2.0u^v## [1] 4 25 216Solution 3
u <- c(5, 6, 7, 8)
v <- c(2, 3, 4)
u + v## Warning in u + v: longer object length is not a multiple of shorter object
## length## [1] 7 9 11 10u - v## Warning in u - v: longer object length is not a multiple of shorter object
## length## [1] 3 3 3 6u * v## Warning in u * v: longer object length is not a multiple of shorter object
## length## [1] 10 18 28 16u / v## Warning in u/v: longer object length is not a multiple of shorter object
## length## [1] 2.50 2.00 1.75 4.00u^v## Warning in u^v: longer object length is not a multiple of shorter object
## length## [1] 25 216 2401 64R uses the recycle rule when vectors have different lengths, i.e. it re-uses elements from the shorter vector (starting at the beginning of the vector). In this case, it treats v as c(2, 3, 4, 2) (re-using its first element 2).
Solution 4
Part a
u <- c(8, 9, 10)
v <- c(1, 2, 3)
w <- 0.5 * v
w <- u + w
w <- w^2
w## [1] 72.25 100.00 132.25Now check with the original approach:
w <- (u + 0.5 * v) ^ 2
w## [1] 72.25 100.00 132.25Part b
w1 <- u + 2
w2 <- u - 5
w <- w1 * w2
w <- w + v
w## [1] 31 46 63Now check with the original approach:
w <- (u + 2) * (u - 5) + v
w## [1] 31 46 63Part c
w1 <- u + 2
w2 <- u - 5
w2 <- w2 * v
w <- w1 / w2
w## [1] 3.333333 1.375000 0.800000Now check with the original approach:
w <- (u + 2) / ((u - 5) * v)
w## [1] 3.333333 1.375000 0.800000Solution 5
Part a
w <- ((u + v) / 2) + u
w## [1] 12.5 14.5 16.5Now check with the original approach:
w <- u + v
w <- w / 2
w <- w + u
w## [1] 12.5 14.5 16.5Part b
w <- (u^3) / (u-v)
w## [1] 73.14286 104.14286 142.85714Now check with the original approach:
w1 <- u^3
w2 <- u - v
w <- w1 / w2
w## [1] 73.14286 104.14286 142.85714Solution 6
The solution for this exercise is available in our eBook Start Here To Learn R – vol. 1: Vectors, arithmetic, and regular sequences.
Solution 7
The solution for this exercise is available in our eBook Start Here To Learn R – vol. 1: Vectors, arithmetic, and regular sequences.
Solution 8
The solution for this exercise is available in our eBook Start Here To Learn R – vol. 1: Vectors, arithmetic, and regular sequences.
Solution 9
The solution for this exercise is available in our eBook Start Here To Learn R – vol. 1: Vectors, arithmetic, and regular sequences.
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