A matrix [A] is defined as 0.125 0.25 0.015625 0.625 0.25 1 0.00463 0.02777 0.16667 1...
12 31 Given a matrix A = (a) (40 pts) Compute the inverse of matrix A by: + Solving Ax=b with b set to [1, 0]T and [0, 1]T + Using Gaussian Elimination with Partial Pivoting (GEPP) (b) (20 pts) Compute the Lo row-sum norm condition number of the matrix A. CS Scanned with CamScanner
Pk $4.00 PL = $2.00 Assume:P $2.00 10 1 15 5 1 28 2 24 6 12 3 20 5 10 4 12 48 7 1 8 2 12 4 4 6 10.5 0.5 0.250.5 7 2 0.5 8 1 0.25 0.5 9 0.5 0.125 0.25 The least cost combination of capital and labor to produce 87 units of output. 0.25 0.13 0.26 8 0.12 90.125 0.06 Pk $4.00 PL = $2.00 Assume:P $2.00 10 1 15 5 1 28...
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
If A is an m × n matrix, and x is an n × 1 vector, then the linear transformation y = Ar maps R" to R", so the linear transformation should have a condition number, condar (x). Assume that |I-ll is a subordinate norm. a. Show that we can define condar (x)-|All llrI/IAxll for every x 0. b. Find the condition number of the linear transformation at[ 2] using the oo-norm. c. Show that condAr(x) IIA for all x....
Probability Distribution For Single Spin X P(X) 4 0.125 3 0.125 2 0.25 1 0.5b b. Calculate the theoretical probability of moving 10 or more spaces in 3 spins (i.e. obtaining the sum of the spins to be 10 or greater). Use your probability distribution in part (a) and note that spins are independent. (Hint: Recognize that getting a 1 on spin 1, a 2 on spin 2, and a 1 on spin 3 is a different result than getting...
Space 1 2 3 4 Weight 0.375 0.25 0.25 0.125 Calculate the theoretical probability of moving 4 or less spaces in 3 spins (i.e. obtaining the sum of the spins to be 4 or less). Use your probability distribution in table above and note that spins are independent. (Hint: Recognize that getting a 1 on spin 1, a 2 on spin 2, and a 1 on spin 3 is a different result than getting a 1 on spin 1, a...
Question 1 a. Define the following matrices in a script file (M-file), ? = ( 8 9 10 11; 23 9 16 15 ;11 12 3 6; 1 2 8 9 ) ? = ( 2 21 7 15; 12 4 8 22; 23 9 5 13; 23 4 21 22) ℎ = (4 9 12 15) b. Add suitable lines of codes to the M-file to do the following. Each of the following points should be coded in only...
10.10 If A is an 'n x n matrix, and x is an n x 1 vector, then the linear transformation y = Ar maps* n to·m, so the linear transformation should have a condition number, condAx (x). Assume that l a subordinate norm a. Show that we can define condar (x)-[All Irl/IArll for every x 0. b. Find the condition number of the linear transformation atx [ - 2 using the oo-norm ng the oo-norm. T-3 2 1 .12...
The question is attached in following two photos. Please use Matlab if you exactly know how to do it. Thank you. Linorm.m Create a function Linorm which takes one argument, M a square matrix and computes the LI-norm of the matrix. This is a number associated to each square matrix M, denoted lIMll, as follows. For each column of the matrix we add together the absolute values of the entries in that column, and we then take the maximum of...
Problem 1. Let the inner product (,) be defined by (u.v)xu (x)v (x) dx, and let the norm Iilbe defined by lIul-)Corhe target funtio), and work with the approximating space P4 Use Gram-Schmidt orthogonalization with this inner product to find orthogonal polynomials (x) through degree four. Standardize your polynomials such that p: (1) 1. (a) Form the five-by-five Gram matrix for this inner product with the basis functions p (x) degree 4 approximation o f (x) using the specified norm,...