6 7 0 1 2 3 - Find A X B A = B = 8 3 4 5 10 11 -2 4- Determining Whether a 3 x 3 Matrix A is Orthogonal or not. A = -1 -2 12 1
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3 - Find A X B
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4- Determining Whether a 3 x 3 Matrix A is Orthogonal or not.
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- Find the value of c that makes matrix A=[101c][110c]defective Select one: a. 2 b. -2 C. 0 d. 1Please solve this question no. 18 also. FromD.s MalikSolving system of linear equations with two variables using Cramer’s rule. In mathematics the coefficientsof linear equations are represented in the form of matrices. A matrix is a two-dimensional array inprogramming. The steps of Cramer’s rule to solve the system of equations are:Step 1: Determining the coefficient matrix from linear equations e.g. a1x+b1y=d1a2x+b2y=d2Coefficient matrix: D = Step 2: Determining the constant column C = Step 3: Finding determinant |D| = (a1*b2) - (b1*a2) and checking if |D| is not equal to zero then do thefollowing: 1. Determining X-matrix: DX = The coefficients of the x−column are replaced by the constant column a1 b1a2 b2d1d2 d1 b1d2 b2 2. Determining Y-matrix: Dy = The coefficients of the Y−column are replaced by the constant column3. To solve for x: x=|DX|/|D|4. To solve for y: y=|Dy|/|D|Note that if |D|=0 then the matrix is singular and solving the system of equationis not possible. You’re required to automate all these steps by writing a program…
- (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.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.%Encode A1, b1 and x1 as the vector of unknowns. A1 = b1 = syms xv1 = %Check the size of A, set it as m1 and n1 [m1,n1] = %Augment A and b to form AM1 AM1 = %Solve the Reduced Rwo Echelon of AM1. RREFA1 = %Collect the last column and set as bnew1, set the remaining elements as Anew1 bnew1= Anew1 = %Check if Anew is an identity matrix, if it is, bnew is the solution if Anew1 =eye(m1,n1) Root1 = bnew1 else display("No Solution") end %Augment the matrix A1 with the identity Matrix of the same size, set the result as AMI1 AMI1 = %Find the reduced row echelon form of AMI1, set the result as RREFAI1 RREFAI1= %Collect the second half of the matrix as AInew1, set the remaining elements as AIold1 AInew1= AIold1 = %Check if AIold1 is an identity matrix, if it is, AInew1 is the inverse %Encode A2, b2 and xv2 as the vector of unknowns. A2 = b2 = syms xv2 = %Check the size of A2, set it as m2 and n2 [m2,n2] = %Augment A2 and b2 to form AM2 AM2 = %Solve the…
- Using Matlab, A=[1 2 3;4 5 6;7 8 10]; a)Create a vector version of the original matrix A. b)Extract those entries of the original matrix A that are greater than 5Draw the following graph as represented in the adjacency matrix below. a b c d A 1 1 1 0 B 0 1 1 0 C 0 0 1 1 d 0 0 0 1Q3 1- Give an example of symmetric matrix . 12 3 21er A=(2 1 3), find AT and |A|. 3 1 2
- Please answer in C++ Create a 2D matrix of dimensions 6 X 5. Take the input from the user to fill this matrix. Find and display the highest value in each column of the matrix.17. Let A and B be two n × n matrices. Show that a) (A + B)^t = A^t + B^t . b) (AB)^t = B^t A^t . If A and B are n × n matrices with AB = BA = In, then B is called the inverse of A (this terminology is appropriate because such a matrix B is unique) and A is said to be invertible. The notation B = A^(−1) denotes that B is the inverse of A.Using MATLAB or Octave Consider the following Matrices: 43 9 74 2 5 6 7 87 35 62 12 A = 1 2 3 B = 15 8 73 9 8 9 0 34 85 9 43 Using single index notation, find the index numbers of the elements in Matrix A that are greater than or equal to 4.