syms x L
lambda = [1 0 0 0;0 1 0 0;1 L L^2 L^3; 0 1 2*L 3*L^3]
lambda =
[ 1, 0, 0, 0]
[ 0, 1, 0, 0]
[ 1, L, L^2, L^3]
[ 0, 1, 2*L, 3*L^3]
A = inv(lambda)
A =
[ 1, 0, 0, 0]
[ 0, 1, 0, 0]
[ 3/(- 3*L^2 + 2*L), (3*L - 1)/(- 3*L^2 + 2*L), -3/(- 3*L^2 + 2*L),
1/(- 3*L^2 + 2*L)]
[ -2/(- 3*L^4 + 2*L^3), -1/(- 3*L^3 + 2*L^2), 2/(- 3*L^4 + 2*L^3),
-1/(- 3*L^3 + 2*L^2)]
C = [0 0 2 6*x]
C =
[ 0, 0, 2, 6*x]
B = C*A
B = [ 6/(- 3*L^2 + 2*L) - (12*x)/(- 3*L^4 + 2*L^3), (2*(3*L
- 1))/(- 3*L^2 + 2*L) - (6*x)/(- 3*L^3 + 2*L^2), (12*x)/(- 3*L^4 +
2*L^3) - 6/(- 3*L^2 + 2*L), 2/(- 3*L^2 + 2*L) - (6*x)/(- 3*L^3 +
2*L^2)]
B1 = 6/(- 3*L^2 + 2*L) - (12*x)/(- 3*L^4 + 2*L^3)
B2 = (2*(3*L - 1))/(- 3*L^2 + 2*L) - (6*x)/(- 3*L^3 + 2*L^2)
B3 = (12*x)/(- 3*L^4 + 2*L^3) - 6/(- 3*L^2 + 2*L)
B4 = 2/(- 3*L^2 + 2*L) - (6*x)/(- 3*L^3 + 2*L^2)
Pr. 2 Consider the Beam Matrix formulation presented in class. Use the definition of Matrix Inverse...
Exercise 1. (a) Find the inverse of the matrix 0 0 1/2 A= 01/ 31 1/5 1 0 (b) Let N be a nxn matrix with N2 = 0. Show (I. - N)-1 = IA+N. (Hint: Use the definition of the inverse.)
Please answer all four questions and show
work.
Find the inverse of each matrix using the reduced row echelon technique. [iii] 20. 2 1 1 [1 1 2 Show that each matrix has no inverse. [-1 2 3] 30. 5 2 0 L 2 -4 -6 For Problems 45-50, use the inverse found in Problem 19. [i 1 -17 19. 3 -1 0 1 2 -3 4 (x + y - z= 6 46.3x – y = 8 ( 2x...
1 -1 -b 1 The inverse of matrix A is (see explanation in Sec. 5.6) and d lo+Go A-1 1 1-blb 1 Thus the solution of the model isx A d, or CISE 4.6 1.Given A-B1--B -t].and c-l 1 0 9 ].find A, e-arnd C -1 3 , find A, 8', and C 2. Use the matrices given in Prob. 1 to verify that 3. Generalize the result (4.11) to the case of a product of three matrices by proving...
Consider a linear system Ax b,and the SVD of the matrix A UXVH (a) please use matrices U, V, 2 to express the pseudo-inverse of the linear system. (b) please show that Av1 1u1, Av2 = 02u2,, Av, a,l,, where ris the rank of the matrix 2 0 (c) If A is a 3x2 matrix A = ( 0 0, calculate its reduced SVD (that is, find its U, 2, V); 0
Consider a linear system Ax b,and the SVD...
(1 Consider the symmetric matrix A = 2 10 2 0 2 2 1. Answer the following questions. 2 3 (1) Find the eigenvalues , , and iz (2 <, <1z) of the matrix A and their corresponding eigenvectors. (2) Find the orthogonal matrix B and its inverse matrix B' that satisfy the following equation: (4 0 0 B-'AB = 0 0 lo o 2) (3) Suppose that the real vectors y and 9 satisfy the following relationship: Show that...
2. (a) Let A be the matrix A -4 21 8 -40 Write down the 3 x 3 permutation matrix P such that PA interchanges the 1st and 3rd rows of A. Find the inverse of P. Use Gaussian elimination with partial pivoting to find an upper triangular matrix U, permutation matrices Pi and P2 and lower triangular matrices Mi and M2 of the form 1 0 0 Mi-1A1 10 a2 0 1 M2 0 0 0 b1 with ail...
can someone confirm these answers for me
To calculate th e inverse of the 2x2 Hilbert matrix ld have! we wou Usually the fraction in front of the matrix would sim is [ 4 2 plify to 12, and the unrounded answer -6 121 but in the proble using the given formula and rounding all fractions to a given number of places Do not round of the rounded determinant. (12 points) t in the problems below, you are asked to...
Material:
8.3.2 Consider the matrix (1 2 3 A-2 3 1 (8.3.28) (i) Use (8.3.27) to find the dominant eigenvalue of A. (ii) Check to see that u-(1 , I , î ), is a positive eigenvector of A. Use 11 and Theorem 8.6 to find the dominant eigenvalue of A and confirm that this is exactly what was obtained in part 0) obtained in part (i) or(ii ii) Compute all the eigenvalues of A directly and confirm the result...
1 L, as a dynamical system (Notes from Assignment #2) We take our definition of dynamical system to be an "object" along with a specific set of modifications that can be performed (dynamically) upon this object. In this case, the object is a bi-infinite straight road with a lamp post at every street corner and a marked lamp (the position of the lamplighter). There are two possible types of modifications: the lamplighter can walk any distance in either direction from...