## Exercises

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?