Vector arithmetic operations are performed element-wise. When adding or subtracting vectors, the result is a vector with the sum or difference of the corresponding elements. When vectors have unequal lengths, the shorter vector is recycled to match the length of the longer vector. Elements in a vector can be accessed using indices inside square brackets. A matrix is a two-dimensional collection of data arranged in rows and columns. Matrix operations like addition, subtraction, multiplication and division are performed element-wise on corresponding elements of the matrices. Elements of a matrix can be accessed and subsets can be extracted using row and column indices inside square brackets. Contour plots show 3D data on a 2D surface using contour lines, and can visualize topographic maps and

1. Vector Maths
Arithmetic operations of vectors are performed member-by-member, i.e., member wise.
For example, suppose we have two vectors a and b.
> a = c(1, 3, 5, 7)
> b = c(1, 2, 4, 8)
Then, if we multiply a by 5, we would get a vector with each of its members multiplied by
5.
> 5 * a
[1] 5 15 25 35
And if we add a and b together, the sum would be a vector whose members are the sum
of the corresponding members from a and b.
> a + b
[1] 2 5 9 15
Similarly for subtraction, multiplication and division, we get new vectors via memberwise
operations.
> a - b
[1] 0 1 1 -1
> a * b
[1] 1 6 20 56
> a / b
[1] 1.000 1.500 1.250 0.875

2. Recycling Rule
• If two vectors are of unequal length, the shorter
one will be recycled in order to match the longer
vector. For example, the following
vectors u and v have different lengths, and their
sum is computed by recycling values of the
shorter vector u.
• > u = c(10, 20, 30)
> v = c(1, 2, 3, 4, 5, 6, 7, 8, 9)
> u + v
[1] 11 22 33 14 25 36 17 28 39

3. Vector Index
• Vector Index
• We retrieve values in a vector by declaring an
index inside a single square
bracket "[]" operator.
• For example, the following shows how to
retrieve a vector member. Since the vector
index is 1-based, we use the index position 3 for
retrieving the third member.
• > s = c("aa", "bb", "cc", "dd", "ee")
> s[3]
[1] "cc"

4. Negative Index
• If the index is negative, it would strip the member
whose position has the same absolute value as
the negative index.
• For example, the following creates a vector slice
with the third member removed.
• > s[-3]
[1] "aa" "bb" "dd" "ee"
• Out-of-Range Index
• If an index is out-of-range, a missing value will be
reported via the symbol NA.
• > s[10]
[1] NA

5. Matrix
• A matrix is a collection of data elements
arranged in a two-dimensional rectangular
layout. The following is an example of a matrix
with 2 rows and 3 columns.
• We reproduce a memory representation of the
matrix in R with the matrix function. The data
elements must be of the same basic type.

6. • > A = matrix(
+ c(2, 4, 3, 1, 5, 7), # the data elements
+ nrow=2, # number of rows
+ ncol=3, # number of columns
+ byrow = T
• A # print the matrix
[,1] [,2] [,3]
[1,] 2 4 3
[2,] 1 5 7RUE) # fill matrix by rows

7. • An element at the mth row, nth column of A can be
accessed by the expression A[m, n].
• > A[2, 3] # element at 2nd row, 3rd column
[1] 7
• The entire mth row A can be extracted as A[m, ].
• > A[2, ] # the 2nd row
[1] 1 5 7
• Similarly, the entire nth column A can be extracted as A[
,n].
• > A[ ,3] # the 3rd column
[1] 3 7
• We can also extract more than one rows or columns at a
time.
• > A[ ,c(1,3)] # the 1st and 3rd columns
[,1] [,2]
[1,] 2 3
[2,] 1 7

8. Matrix Addition & Subtraction
• # Create two 2x3 matrices.
• matrix1 <- matrix(c(3, 9, -1, 4, 2, 6), nrow = 2)
print(matrix1)
• matrix2 <- matrix(c(5, 2, 0, 9, 3, 4), nrow = 2)
print(matrix2)
• # Add the matrices.
• result <- matrix1 + matrix2
• cat("Result of addition","n")
• print(result)
• # Subtract the matrices
• result <- matrix1 - matrix2
• cat("Result of subtraction","n") print(result)

9. Matrix Multiplication & Division
• # Create two 2x3 matrices.
• matrix1 <- matrix(c(3, 9, -1, 4, 2, 6), nrow = 2)
print(matrix1)
• matrix2 <- matrix(c(5, 2, 0, 9, 3, 4), nrow = 2)
print(matrix2
• # Multiply the matrices.
• result <- matrix1 * matrix2
• cat("Result of multiplication","n")
print(result))

10. • # Divide the matrices
• result <- matrix1 / matrix2
• cat("Result of division","n")
• print(result)

11. Matrix Access
• Create a Matrix
• x<-1:12
• Print(x)
• Mat<-matrix(x,3,4)
• Access third row of an existing matrix
• Mat[3,]
• Second column
• Mat[,2]
• Access second and third column
• Mat[,2,3]

12. Contour plot
• Contour plots are used to show 3-
dimensional data on a 2-dimensional surface.
The most common example of a contour plot
is a topographical map, which shows latitude
and longitude on the y and x axis, and
elevation overlaid with contours. Colours can
also be used on the map surface to further
highlight the contours

13. • Create a matrix, mat which is 9 rows and 9 columns with
all values are 1
• Mat<-matrix(1,9,9)
• Print(mat)
• Replace a value of 3rd row 3rd column
• Mat[3,3]<-0
• Contour(mat)
• Create a 3D perspective plot with persp(). It provides 3D
wireframe plot
• Persp(mat)
• R includes some pre defined data sets
• Volcano, which is 3D map dormant of New Zealand
• Contour(volcano)
• Heat map
• Image(volcano)