12. Perform Gauss-Jordan elimination on the augmented matrix shown. 1 0 2 A.0 17 0 0 1 10 0 B. 0 10 0 0 1 -4 2 C. -1 -26 10 3. D. 0 1 -7 2370
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- Consider the matrix A defined as: [1 0 1] A=[1 2 2] [1 2 1] 121 Compute the determinant of A. Detail each of the computation steps. Compute the inverse of A: A−1 (refer to ”Wiki: adjoint matrix” for the computation of the adjoint matrix A∗).Observe the following two Sequential Search and Binary Search algorithms in the image. Perform a comparative analysis of the Sequential Search and Binary Search algorithms in terms of the number of basic operations executed by the two algorithms. A. Calculate and analyze the time complexity T(n) and the efficiency class of the two search algorithms in the worst case. B. Write an example case by writing down the elements for different data sizes, for example n=4, 8, ... Please specify the elements of table A and the data you are looking for, x. Write an illustration of the comparison process for every n to confirm the complexity of the algorithm in point a). C. Describe your opinion regarding the comparative analysis of the efficiency of the two algorithms! Please solve subparts A,B,C in 60 minutes ASAP can u get thank uCan you help me with a MATLAB code? I want to multiply a 3x3 matrix to every vector of a 3x101 matrix. Can you create some type of loop to help with that? For example, If I had A = [1 0 0; 0 2 0; 0 0 3]; and B = [1 2 3; 4 5 6; 7 8 9; 10 11 12; ...];. I would want to multiply matrix A to every row vector of B to get another matrix.
- %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…Write down the tensor expression for the following matrix operations. Where A,B are 3 × 3, C is 3 × 4, and D is 4 × 7 matrices. And for a matrix M, its i-th row j-th column component will be denoted as M_ij . (a) det(A · B^T ).(b) Tr[A · B].(c) B · C · D, and explicitly spell out all the index summation.(d)δ_ii =?(e) ϵ_ijkϵ_ijk =?QUESTION ONE (20 MARKS)1.1 Consider the state space graph shown below. P is the start state and V is the goal state. The costs for each edge are shown on the graph. Each edge can be traversed in both directions.1.1.1 Use Breadth-First Search to generate the shortest path from P to V. (10)1.1.2 Apply the Depth First Search method to find a path from P to V. (10)QUESTION TWO (20 MARKS)2.1 Compute the truth table for the following expressions and their subexpressions.2.1.1 (p → q) ≡ (NOT p OR q) (5)2.1.2 p → (q → (r OR NOT p)) (5)2.1.3 (p OR q) → (p AND q) (5)2.1.4 (p AND q) → (p OR r) (5)QUESTION THREE (10 MARKS)3.1 The binary exclusive-or function, ⊕, is defined to have value TRUE if and only if exactly one of its arguments are TRUE.3.3.1 Draw the truth table for ⊕. (5)3.3.2 Is ⊕ commutative? Is it associative? (5)PQRSTVUQUESTION FOUR (20 MARKS)4.1 Translate the following sentences into a Prolog program (10)Everyone who teaches programming module is smart.Craig teaches the programming…
- Classify the 1’s, 2’s, 3’s for the zip code data in R. (a) Use the k-nearest neighbor classification with k = 1, 3, 5, 7, 15. Report both the training and test errors for each choice. (b) Implement the LDA method and report its training and testing errors. Note: Before carrying out the LDA analysis, consider deleting variable 16 first from the data, since it takes constant values and may cause the singularity of the covariance matrix. In general, a constant variable does not have a discriminating power to separate two classes.Using Matlab answer this question : Create a 3x3 matrix after it makes a matrix that computes the inner products between rows and columns, using the * operator.confirm that a matrix times its inverse returns the identity matrix:Is a rank of a matrix can be zero and what is nullity of a matrix?Matlab question
- Write a matlab code for Creating 5x5 matrix with rank 4 and generate 2 vectors each that are not in a. Column space b. Rowspace c. Left null space d. Right null space Explain how will you verify your answer for various cases in above problem5 Consider the degree-4 LFSR given by x to the power of 4 space plus space x squared space plus space x space plus space 1. Assume that the LFSR is initialized with the string left parenthesis s subscript 0 s subscript 1 s subscript 2 s subscript 3 right parenthesis equals left parenthesis 0110 right parenthesis. How long is the cycle generated?(20pts) Consider the matrixA =−2 11−10 5(a) Determine, by hand, an SVD of A, A = UΣVT. The SVD is not unique,so find the one with the minimum number of minus signs in U and V . List thesingular values σ1 and σ2, and the left and right singular vectors.(b) Find A−1 not directly, but via the SVD. Check your result by typing inv(A)in MATLAB or calculating A−1 by other methods.(c) Find the eigenvalues λ1 and λ2 of A. Verify that detA = λ1λ2 and |detA| =σ1σ2