Question 5. Given the tridiagonal matrix 1.96 0.9996 0.19 1.8469 0.4025 0.69 1.4087 0.1125 0.98 2.0882 work out the values l;, i = 1, 4 and ui, i = 1,..., 3 in the LU factorisation A = LU with %3D ... 11 [1 ul 0.19 12 1 u2 L = 0.69 13 1 u3 0.98 14 1 Use the LU factorisation to solve the system Ax b with 7.762776 7.048489 0.326538 4.649794. for xi, i = 1, ...,4 Use at least 6 decimal places for your calculations and specify your final results to 2 decimal places. (a) l1 ),l4 %3D %3D (b) u1 , U2 = U3 = (c) x1 , X2 = , X4 = , X3 =

Question 5. Given the tridiagonal matrix 1.96 0.9996 0.19 1.8469 0.4025 0.69 1.4087 0.1125 0.98 2.0882 work out the values l;, i = 1, 4 and ui, i = 1,..., 3 in the LU factorisation A = LU with %3D ... 11 [1 ul 0.19 12 1 u2 L = 0.69 13 1 u3 0.98 14 1 Use the LU factorisation to solve the system Ax b with 7.762776 7.048489 0.326538 4.649794. for xi, i = 1, ...,4 Use at least 6 decimal places for your calculations and specify your final results to 2 decimal places. (a) l1 ),l4 %3D %3D (b) u1 , U2 = U3 = (c) x1 , X2 = , X4 = , X3 =

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

H3.
Jj.34.
3. In the configuration illustrated in Fig. 1 the camera matrices are P₁ = [10] and Pr = [I t], where I is the identity matrix and t = (-6, 0, 0). The point Q has coordinates (3, 0, 3)T. Assume b = 6 cm, f = 1 cm. Compute the image of Q in unit of cm on the image plane of the camera on the left and the corresponding epipolar line on the image plane of the camera on the right. Z X1 b A Fig. 1 P = (Xp, Yp, Zp) X
9
find the single matrix equal to the following
Help me please
Question 30.4 In terms of X,Y and Z find the matrix A if you are given the following: (5ZA'X)" = Y
Note:- • Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. • Answer completely. • You will get up vote for sure.
1. Consider the following matrix: The SVD of this matrix is U= Σ = v= A = 1.0723 2.1690 2.7877 1.1307 3.9083 4.7857 6.2692 1.8343 7.0398 8.0931 8.8831 0.0720 L0.0207 – 1.9516 0.9392 4.0374] 0.1753 0.7666 0.5781 -0.2179 -0.5263 0.2606 0.3434 -0.7329 -0.8218 0.2006 -0.4278 0.3184 0.0113 0.9280 -0.3338 0.1654 16.8964 0 0 0 0 4.9197 0 (a) What is the rank of A? (b) By A, construct a matrix of rank 2. 0 0 0 1.0101 0 0 0 [-0.4780 0.0379-0.8460 -0.2334] -0.5720 0.3673 0.4902 - 0.5456 -0.6627 -0.2464 0.1743 0.6854 -0.0725 -0.8961 0.1172 0.4220] (c) Let B = o₁u₁v₁, where σ₁ is the (1,1) entry of the matrix Σ, i.e., Σ(1,1)= 0₁, the vectors U₁ and v₁ are the first column of the matrices u and v, respectively. Without directly computing, find the value of ||A - B||F?
Problem 6. given by Prove the Woodbury matrix identity (eq. (1.111) in textbook) (A + UBV)¯¹ = A¯¹ – A¯¹U(B¯¹ + VA¯¹U)¯¹VA¯¹
D Question 16 Find the dimensions of the null space and the column space of the given matrix. A= 10 7 1 5 1 -2-4-5-4 1 O dim Nul A = 4, dim Col A = 1 O dim Nul A=2, dim Col A = 3 O dim Nul A-3, dim Col A = 2 O dim Nul A-3, dim Col A = 3 Question 17