1. Define H as a vector linearly spaced values between -20 and 20. Use a decrement of 0.4 between the values. Define S1 and S2 as tan and cos values of H. Create a line plot of both sets of data.
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- Create a row vector of 1's that has 4 rows. Now Create a column vector of 1's that has 4 columns. Using matrix multiplication, multiply both of these to get a 4x4 matrix and display the resulting matrix. Using matlab, do this. Please answer it correctly and don’t copy from anywhere otherwise it will be downvoted.Create a 3-by-3 matrix: A = [1 2 3;4 5 6;7 8 10] (a)Extract a submatrix B consisting of rows 1 and 3 and columns 1 and 2 of the matrix A (b)Interchange rows 1 and 3 of A and put it in a variable C. Hint: use the vector of row indices together with the colon operator (c)Create a vector version of the original matrix A. (d)Delete the 2nd column of the original matrix A and put it in a variable called A. (e)Insert a 2nd column to the new matrix A to restore it back to its original form A. (f) Extract those entries of the original matrix A that are greater than 5What 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…
- Create a MATLAB function file that solves matrices with the following conditions: a. Create a 4 x 4 vector C (range of vector numbers should be multiples of 3) b. Find the sums of columns 1 and 2 of C c. Find a version of C with rows 2 and 4 d. Display the fourth column of transpose C3. 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)Matlab screenshot - If x=[ 2 6 12; 15 6 3; 10 11 1], then a) replace the first row elements of matrix x with its average value. b) reshape this matrix into row 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.Fill in the blank to calculate the inverse of mm = [8 1 6; 3 5 7; 4 9 2];inverse1 = _______ Question 1 options: inverse(m) cross(m) inv(m) rref(m) I need to find a vector that is perpendicular to two other vectors. I need... Question 2 options: Matrix multiplication The transpose The dot product The cross product If v and w are vectors of equal length then I run this codex = dot(v,w) Question 3 options: x is a vector the same length as v and w x is a single number How can I verify that two vectors named v and w are perpendicular? Question 4 options: They are perpendicular if v*w equals w*v They are perpendicular if cross(v,w) equals 0 They are perpendicular if dot(v,w) equals 0 They are perpendicular if v*w is an identity…Write a program that fills a 5 x 5 matrix with the following data: Upper left triangle with -1 Lower right triangle with 1 Right to left diagonal with 0
- (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.6. A three-dimensional vector has the form: A = (x, y, z) can be represented as: given the vectors: Example: Their sum is:Example: struct VECTOR { double x; double y; double z; }; A = ( a, b, c ) (5, 6, 2) and B = ( d, e, f ) (3, 1,9) A + B = ( a + d, b + e, c + f ) (5 + 3, 6 + 1, 2 + 9) = (8, 7,11)A B = a x d + b x e + c x f Their scalar product is:(result is a scalar) example: 5 x 3 + 6 x 1 + 2 x 9 = 39 Write the complete definition code for the functions: a. calc_sum computes and returns the sum of two vectors b. scalar_prod computes and returns the scalar product of two vectorsPlease Help me With This Problem Write a function to find the norm of a matrix. The norm is defined as the square root of the sum of squaresof all elements in the matrix
