MATLAB and R Programming (ME-705) - Important Questions

Write an M-file that reads an $n\times n$ matrix, extracts its main diagonal and returns the sum of diagonal elements (handle complex entries).

In MATLAB, generate a random complex vector $z$ of length 100, compute $\sum z$ and plot $\mathrm{real}(z)$ vs $\mathrm{imag}(z)$. Provide the script and explain steps.

Using R, create a data frame with numeric and factor columns, show how to append a new row and subset only rows where a factor has a given level.

Explain differences between MATLAB matrices and R data frames. Provide examples where each structure is preferable (include short code snippets: MATLAB and R).

Demonstrate plotting in MATLAB: plot a parametric curve with $x=\cos(t)$ and $y=\sin(2t)$ for $t\in[0,2\pi]$, label axes and add a legend.

In R, create a $3\times 3$ matrix, print it, add a new column and extract the submatrix consisting of rows 1 to 2 and columns 2 to 3. Show the R commands and output.

Write an R snippet to convert a numeric vector into a factor with specified levels, explain how factors differ from continuous variables and show how to reorder factor levels.

Describe the MATLAB environment and basic commands. Give examples of creating variables, listing the workspace, clearing variables, saving workspace, and write a short script that performs matrix multiplication.

Write an M-file that reads a character string, converts all lowercase letters to uppercase and returns the ASCII codes of the converted string. Include handling for non-alphabetic characters.

Explain installation and setup steps for R and RStudio. Demonstrate R data types and show examples of arithmetic and logical operators with short code snippets.