Lab week 10

This lab is dedicated to working with matrices. The following matrix B can be used for exercises.

B <- matrix(
  c(1, 2, 3, 
    4, 5, 6, 
    7, 8, 9), 
  nrow = 3, ncol = 3
)

B

     [,1] [,2] [,3]
[1,]    1    4    7
[2,]    2    5    8
[3,]    3    6    9

1. Show examples of element-wise operations, matrix multiplication, transposition, joining and sub-setting.

2. Try to find the inverse of B and find the determinant.

3. Modify the first element in B such that the matrix is invertible and find the inverse.

4. Define a matrix from the mtcars data set and build a regression model that predicts miles per gallon based on the number of cylinders, horsepower, axle ratio, weight and acceleration time.