Simple tasks in R language.

Task 1: a) Given vectors v=(4, -5, 12, 7, -4, 2) and w=(0, 3, -2, 12, 22, 0). Create matrix M from these vectors: 4 0 -5 3 12 -2 7 12 -4 22 2 0 b) Remove the second column from the matrix M and replace all elements on the main diagonal that are less than 5 with 3. c) Solve the system of equations Mx = b, where b consists of the first three elements of v. Round the solution vector to three decimal places and specify its average value. d) Concatenate the following two vectors so that they correctly display the names of the scientists: X = (“Lise”, “Marie”, “Rosalind”, “Ann”), Y = (“Franklin”, “Tsukamoto”, “Curie”, “Meitner”). e) Indicate all names and surnames from the previous task that contain the letter E/e or M/m. f) Create a list X with the following elements: Op = "+" A = (3, 6, 9, 12) B = (1, 2, 3, 4) g) Create an expression that applies the operation specified in Op (addition) to vectors A and B. Then change the value of Op to "-" and use the same expression to create the difference. Save the difference in vector D. Task 2: a) Create an object obj, which, upon requesting its structure, provides the following response: > str(obj) List of 4 $ O: int [1:3, 1:3] 1 4 7 2 5 8 3 6 9 ..- attr(*, "dimnames")=List of 2 .. ..$ : chr [1:3] "a" "b" "c" .. ..$ : chr [1:4] "C" "D" "E" $ P: List of 2 .. ..$ TUD: chr [1:3] "T" "U" "D" .. ..$ Jahr: num 2023 $ Q: logi [1:6] TRUE FALSE FALSE TRUE TRUE TRUE $ M: Named int [1:6] 1 2 3 4 5 6 ..- attr(*, "names")=chr [1:6] "Jan" "Feb" "Mar" "Apr"... b) Explain why this object cannot be an array (Array). Provide at least two reasons. c) Select the vector TUD from the list obj in three different ways. d) Find the result of multiplying matrices: the second and third columns of the modified Matrix O and the matrix 8 4 6 2 Find the difference between the largest and smallest values of the resulting matrix after multiplication and indicate this difference.