Matrices

  1. Make a 5x3 matrix (5 rows, 3 columns) using matrix( ).

Ex: matrix(1:6,nrow=3,ncol=2) makes a 3x2 matrix using numbers between 1 and 6.

  1. What happens when you use byrow = TRUE in your matrix( ) as an additional argument? Assign the matrix to a variable m.
  1. Extract the first 2 columns and first 3 rows of your matrix using [ ] notation.
  1. Extract the last two rows of the matrix you created previously.
  1. Multiplication table: write an R code to print out the 9x9 multiplication table.
  1. Create a vector x containing numbers from 1 to 15 and a vector y containing numbers from 24 to 35. Can you combine these vectors into a matrix? Explain the result.
  1. Create a new matrix called M by selecting all rows except the last 3 and all the columns from the previous matrix. Evaluate the numbers of rows and columns of the matrix.
  1. Assign rownames and colnames to M.
  1. Create a logical matrix (mix TRUE and FALSE values) L of same dimensions as M.

Sum L and M. What happened? Comment the result.

Finally, multiply L and M and explain the result.

  1. Perform the algebric matrix multiplication of L and M
  1. Generate different vectors:
    • 13 random numbers with mean = 6, sd = 3
    • 13 random numbers uniformly distributed between -30 and 140
    • a logical vector identifying the numbers in the first vector that are > 4.5
    • a logical vector identifying the numbers in the first vector that are, in absolute value, < 8
    • a logical vector identifying the numbers in the second vector that are, in absolute value, > 20 and negative
    • a vector containing the sum between the first vector and the second vector
    • a vector containing the multiplication between the third vector and the fourth vector

Create a matrix binding all the vectors by row, evaluate the dimensions, traspose it and evaluate the dimensions again.

  1. Create a numeric 5x5 matrix, containing numbers from 1 to 5. Transform the matrix in a upper triangular matrix by assigning to the lower triangle NA values. Then:
    • Extract the values on the diagonal
    • Extract the value in the third column and second row.
    • Extract values in the fourth column.
    • Extract values in the fifth row and assign them to a vector a.
    • Print the positions of the vector a in which the number 5 is found.
    • Create a logical vector b by testing whether the values in a are contained in c(1,3)
    • Use the vector b to extract from the fifth column of the matrix the values where b is TRUE