D) If x = [1, 5, 7, 9, 13, 20, 6, 7, 8], replace the first five elements of vector x with its maximum value. E) Let x = [3 2 6 8] and y = [4 1 3 5] .Divide each element of y by the corresponding
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![D) If x= [1, 5, 7, 9, 13, 20, 6, 7, 8], replace the first five elements of vector x with its
maximum value.
E) Let x = [3 2 6 8] and y = [4 1 3 5] .Divide each element of y by the corresponding](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F996e9e0c-a42f-40c1-a1a5-670c9403afa0%2Ff6d91cb3-8ffc-44e8-9532-d29668df77b1%2Fqkhii4e_processed.jpeg&w=3840&q=75)
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- Consider a vector ('L', 'M', 'M', 'L', 'H', 'M', 'H', 'H'), where H stands for ‘high’, L stands for ‘low’, and M for ‘medium’ in rstudio. a. Convert this vector into an unordered factor. b. Convert this vector into an ordered factor with Low < Medium < High.Let y be a column vector: y = [1, 2, 3, 4, 5, 6] so that y.shape = (6,1). Reshape the vector into a matrix z using the numpy.array.reshape and (numpy.array.transpose if necessary) to form a new matrix z whose first column is [1, 2, 3], and whose second column is [4, 5, 6]. Print out the resulting array z.For input vector x, write a function to check whether there exists at most 5 elements in x whose values are less than 7.
- Consider the vector: x = c(1,2,3,4). What is the value of (x+2)[(!is.na(x)) & x > 0]? What do you find?Given 2,3,4,1,5. What happens if it undergoes the following function? Function Shift(vector,i,j) If i ≤ j then Return vector End if Store<- vector[i] For 0≤k≤(i-j-1) do Vector[i-k]<-vector[i-k-1] End for Vector[j]<-store End function Shift (vector,5,3) Shift (vector,3,1)(Sparse matrix–vector product) Recall from Section 3.4.2 that a matrix is said to be sparse if most of its entries are zero. More formally, assume a m × n matrix A has sparsity coefficient γ(A) ≪ 1, where γ(A) ≐ d(A)/s(A), d(A) is the number of nonzero elements in A, and s(A) is the size of A (in this case, s(A) = mn). 1. Evaluate the number of operations (multiplications and additions) that are required to form the matrix– vector product Ax, for any given vector x ∈ Rn and generic, non-sparse A. Show that this number is reduced by a factor γ(A), if A is sparse. 2. Now assume that A is not sparse, but is a rank-one modification of a sparse matrix. That is, A is of the form à + uv⊤, where à ∈ Rm,n is sparse, and u ∈ Rm, v ∈ Rm are given. Devise a method to compute the matrix–vector product Ax that exploits sparsity.
- Demonstrate how to use pop_back function in vector C++. Given vector<int> v ={1,7,9,3,5,8}. Remove last element in the vector using pop_back and print the vector.Problem 1) Change the diagonal elements of a 3X3 matrix to 1. Diagonal elements of the example matrix shown here are 10, 8, 2 10 -4 0 7 8 3 0 0 2 Read the given values from input (cin) using for loops and then write your code to solve the diagonal.Write a function linear_independence that takes a collection of vectors with integer entries (each written as a list), and returns True if this collection of vectors is linearly independent, and False otherwise. Examples: linear_independence([1,2]) should return True. linear_independence([1,3,7],[2,8,3],[7,8,1]) should returnTrue. linear_independence([1,3,7],[2,8,3],[7,8,1],[1,2,3]) should return False.
- 3. Use two vectors and make them into one. Use the following vectors:Vector#1 {1, 1, 5, -3, 0}Vector#2 {9,7,2}Return a vector containing 1, 1, 5, -3, 0, 9, 7, 2 (in that order)IN PYTHON! Given an n×n matrix A and n×1 right-hand side b, write a function that carries out q iterations of the Gauss elimination outer loop (without pivoting), where q is an integer between 1 and n, and returns the resulting augmented matrix with all below-diagonal elements transformed to zero in the left-most q columns. ##The code format given below may help # def gaussq (A, b, q): '''Apply Gauss elimination (without pivoting) to first q columns of a given linear system Inputs: A, coefficient matrix, size n by n b, vector of constants, n by 1 q, number of columns to apply Gauss elimination to, an integer between 1 and n Output: Aa, augmented matrix with all below-diagonal elements transformed to zero in the left-most q columns, n by n+1 #to check the workWhat to input here to run properly? % Encode the Matrix A and the column vector b. A= b= % Solve for Determinant of A. Set as dA. dA = % Find the Inverse of A. set as iA. iA = % Form the Reduced Row Echelon of A. Set as rA. rA= %Find the number of rows and number of columns of Ab. set as rowA and colA. % Find the sum of the columns of A. Set as SumA. %In each of the columns of A, find the highest values and its indices.Set as highA and locA. %Augment A with b; Set as Ab. % Find b\A. Set as Root1. %Form the Reduced Row Echelon Form of Ab. Set as refAb. %Extract the last column of refAb.Set as Root2. %Create a matrix A whose elements are the same as matrix A, but the first column is the column vector b. Set as Ax. %Create a matrix A whose elements are the same as matrix A, but the second column is the column vector b. Set as Ay. %Create a matrix A whose elements are the same as matrix A, but the third column is the column vector b. Set as Az. %Create…
