1. Suppose X is a matrix in R. Which of the following is not equivalent to X?
    • A) t( t(X) )
    • B) X %*% matrix(1,ncol(X) )
    • C) X*1
    • D) X%*%diag(ncol(X))
  2. Solve the following system of equations using R:

    What is the solution for $$c$?

  3. Load the following two matrices into R:

     a <- matrix(1:12, nrow=4)
     b <- matrix(1:15, nrow=3)

    Note the dimension of a and the dimension of b.

    In the question below, we will use the matrix multiplication operator in R, %*%, to multiply these two matrices.

    What is the value in the 3rd row and the 2nd column of the matrix product of a and b?

  4. Multiply the 3rd row of a with the 2nd column of b, using the element-wise vector multiplication with *.

    What is the sum of the elements in the resulting vector?