Matrix exercises

November 28, 2015

(This article was first published on R-exercises, and kindly contributed to R-bloggers)

Please note, solutions are available here.
Exercise 1
Create three vectors  x,y,z  with integers and each vector has 3 elements. Combine the three vectors to become a 3×3 matrix  A  where each column represents a vector. Change the row names to  a,b,c.
Think: How about each row represents a vector, can you modify your code to implement it?

Exercise 2
Please check your result from Exercise 1, using  is.matrix(A). It should return  TRUE, if your answer is correct. Otherwise, please correct your answer. Hint: Note that  is.matrix()  will return  FALSE  on a non-matrix type of input. Eg: a vector and so on.

Exercise 3
Create a vector with 12 integers. Convert the vector to a 4*3 matrix  B  using  matrix(). Please change the column names to  x, y, z  and row names to  a, b, c, d.
The argument  byrow  in  matrix()  is set to be  FALSE  by default. Please change it to  TRUE  and print  B  to see the differences.

Exercise 4
Please obtain the transpose matrix of  B  named  tB .

Exercise 5
Now  tB  is a 3×4 matrix. By the rule of matrix multiplication in algebra, can we perform  tB*tB  in R language? (Is a 3×4 matrix multiplied by a 3×4 allowed?) What result would we get?

Exercise 6
As we can see from Exercise 5, we were expecting that  tB*tB  would not be allowed because it disobeys the algebra rules. But it actually went through the computation in R. However, as we check the output result , we notice the multiplication with a single  *  operator is performing the componentwise multiplication. It is not the conventional matrix multiplication. How to perform the conventional matrix multiplication in R? Can you compute matrix  A  multiplies  tB ?

Exercise 7
If we convert  A  to a  data.frame  type instead of a  matrix , can we still compute a conventional matrix multiplication for matrix  A  multiplies matrix  A ? Is there any way we could still perform the matrix multiplication for two  data.frame  type variables? (Assuming proper dimension)

Exercise 8
Extract a sub-matrix from  B  named  subB . It should be a 3×3 matrix which includes the last three rows of matrix  B  and their corresponding columns.

Exercise 9
Compute  3*A ,  A+subB ,  A-subB . Can we compute  A+B? Why?

Exercise 10
Generate a n * n matrix (square matrix)  A1  with proper number of random numbers, then generate another n * m matrix  A2.
If we have  A1*M=A2  (Here * represents the conventional multiplication), please solve for  M.
Hint: use the  runif()  and  solve()  functions. E.g.,  runif(9)  should give you 9 random numbers.

Image: “200px-Sudoku06u” by DrBorka from nl. Licensed under CC BY-SA 3.0 via Wikimedia Commons.

To leave a comment for the author, please follow the link and comment on their blog: R-exercises. offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...

If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Comments are closed.

Search R-bloggers


Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)