R Exercises | Programming Exercises for Finance in the R Language

Math and Stats: Exercises

7. Matrix rank. The rank of a matrix is the same as the rank of its transpose. In this exercise, you are given a matrix, X. Check its rank using the rankMatrix() function from the Matrix library. After that, transpose it using the t() function and check its rank.



                                X <- matrix(c(0,1,0,0,2,0,1,3,4), nrow=3, ncol=3)



                            # Import the Matrix library.
                            library(___)

                            # Compute the rank of X.
                            X_rank <- ___(X)

                            # Transpose X.
                            X_transpose <- ___

                            # Compute the rank of X_transpose.
                            X_transpose_rank <- ___



                            # Import the Matrix library.
                            library(Matrix)

                            # Compute the rank of X.
                            X_rank <- rankMatrix(X)

                            # Transpose X.
                            X_transpose <- t(X)

                            # Compute the rank of X_transpose.
                            X_transpose_rank <- rankMatrix(X_transpose)


                            test_error()
                            test_function("library", incorrect_msg="Did you import the correct library?")
                            test_function("rankMatrix", incorrect_msg="Did you use `rankMatrix()` to compute the rank of `X`?")
                            test_object("X_transpose", incorrect_msg="Did you compute the transpose of `X`?")
                            success_msg("Excellent work. Given your findings, was X a full rank matrix?")

You can use the rankMatrix() function to check a matrix's rank.

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