1 Problem 7 Let A 4 5 - 1 5 0 2 -1 2 3 -4 7 2 1 3 7 2 -4 2 0 0 10 1 1 a) (4 pts] Using the [V, DJ command in MATLAB with rational format, find a diagonal matrix D and a matrix V of maximal rank satisfying the matrix equation A * V = V * D. Is A real-diagonalizable? b) (4 pts) Write down the eigenvalues of A. For each eigenvalue,...
4 7 5 0 2 2 Problem 7 Let A= -1 2 9 -4 1 5 -1 3 7 3 1 -4 2 0 1 1 0 10 2 a) (4 pts] Using the [V, D] command in MATLAB with rational format, find a diagonal matrix D and a matrix V of maximal rank satisfying the matrix equation A * V = V * D. Is A real-diagonalizable? b) [4 pts) Write down the eigenvalues of A. For each eigenvalue,...
03:25 pts) For the edge weight matrix assigned to you for a directed graph, determine the shortest path weights between any two vertices of the graph using the Floyd-Warshall algorithm. Show clearly the distance matrix and the predecessor matrix for each iteration Also, extract a path of length two or above between any two vertices of your choice. Clearly show the path extraction steps, as shown in the slides. V1 V1 9 V2 0 V3 3 w 85 V2 V3...
5. (a) (10 pts) Find the eigenvalues of A= 4 -5 8 0 3 0 -1 3 -2 (b) (6 pts) Find a basis for any one of eigenspaces of A (you may use any eigenvalue you have found in (a)).
[3] (25 pts : (a) 10 pts (b) 10 pts (c) 5 pts) Let X1, X2, ..., X. (n > 2) denote a random sample from a shifted exponential population E(Mo) with pdf f(1; 4,0) = o-'exp(-(x -- }/)||4,00) (1) where - < < oo and a > 0 are unknown. o(a) Find the MLE (AMLE,GMLE) of 0 =(1,0). (b) Find the MLE of MLE of n = Puc (X1 > a) = exp{-(a – 4)+/o} the reliability at a,...
1. Given 1 A= -10 -1 0 0 32 BE 0 03 3 O 3 a. Find eigenvalues and eigenvectors of A. Is it invertible? b. For each eigenvalue indicate its algebraic and geometrical multiplicity, and state its eigenspace Eig(A) c. Diagonalize A if possible B d. Find B
now please (10 pts) 3. Let 0-3 8 A= -3 5 - 1 2 -5 Solve the equation (find the general solution) for Ax-2x. cos e 2-sin -cos e 2+ sin e (25 pts) 4. a) (5 pts) Find det (B) and the inverse of B, where R
4 0 2 7) Find the eigenvalues of the matrix A= 1-2 3-4 0 0 - Clearly show your work. (15 points) 3
5 3 1 0 Problem 10 Let wi = ,W2 W3 Let W = Span{W1,W2, W3} C R6. 11 9 1 2 a) [6 pts] Use the Gram-Schmit algorithm to find an orthogonal basis for W. You should explicitly show each step of your calculation. 10 -7 11 b) [5 pts) Let v = Compute the projection prw(v) of v onto the subspace W using the 5 orthogonal basis in a). c) (4 pts] Use the computation in b) to...
(9) (5 + 10 pts) Describe what it means for two graphs to be isomor- phic. Check whether the following two graphs are isomorphic or not. b4 b5 b6 04 + 05 + 06 x a1 02 03 bi b2 b3 (10) (10 pts) Prove or disprove the identity. x (y+z) = (x @y)+ ( 12) (10 pts) find the Boolean function that satisfies the following truth table. 1 X Y Z F(x, y, z) 111 0 110 101 0...