Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 4.5, Problem 7E
To determine
To prove that the number of real solution (x, y, K).
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5. The volume V of a given mass of
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S
(d)90
Consider a matrix
3
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Define matrix B as transpose of the inverse of matrix A. Find the determinant of matrix A + B.
For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical).
Year Month Rate (%)2009 Mar 8.72009 Apr 9.02009 May 9.42009 Jun 9.52009 Jul 9.52009 Aug 9.62009 Sep 9.82009 Oct 10.02009 Nov 9.92009 Dec 9.92010 Jan 9.82010 Feb 9.82010 Mar 9.92010 Apr 9.92010 May 9.62010 Jun 9.42010 Jul 9.52010 Aug 9.52010 Sep 9.52010 Oct 9.52010 Nov 9.82010 Dec 9.32011 Jan 9.12011 Feb 9.02011 Mar 8.92011 Apr 9.02011 May 9.02011 Jun 9.12011 Jul 9.02011 Aug 9.02011 Sep 9.02011 Oct 8.92011 Nov 8.62011 Dec 8.52012 Jan 8.32012 Feb 8.32012 Mar 8.22012 Apr 8.12012 May 8.22012 Jun 8.22012 Jul 8.22012 Aug 8.12012 Sep 7.82012 Oct…
Chapter 4 Solutions
Numerical Analysis
Ch. 4.1 - Solve the normal equations to find the least...Ch. 4.1 - Find the least squares solutions and RMSE of the...Ch. 4.1 - Find the least squares solution of the...Ch. 4.1 - Let mn, let A be the mn identity matrix (the...Ch. 4.1 - Prove that the 2-norm is a vector norm. You...Ch. 4.1 - Let A be an nn nonsingular matrix. (a) Prove that...Ch. 4.1 - Find the best line through the set of data points,...Ch. 4.1 - Find the best line through the set of data points,...Ch. 4.1 - Find the best parabola through each data point set...Ch. 4.1 - Find the best degree 3 polynomial through each set...
Ch. 4.1 - Assume that the height of a model rocket is...Ch. 4.1 - Given data points...Ch. 4.1 - Form the normal equations, and compute the least...Ch. 4.1 - Prob. 2CPCh. 4.1 - Prob. 3CPCh. 4.1 - Prob. 4CPCh. 4.1 - 5. A company test-markets a new soft drink in 22...Ch. 4.1 - What is the slope of the parabola y=x2on[ 0,1 ] ?...Ch. 4.1 - Find the least squares (a) line (b) parabola...Ch. 4.1 - Let A be the 10n matrix formed by the first n...Ch. 4.1 - Prob. 9CPCh. 4.1 - The following data, collected by U.S. Bureau of...Ch. 4.2 - Fit data to the periodic model...Ch. 4.2 - Fit the data to the periodic models...Ch. 4.2 - Fit data to the exponential model by using...Ch. 4.2 - Prob. 4ECh. 4.2 - Fit data to the power law model by using...Ch. 4.2 - Prob. 6ECh. 4.2 - Fit the monthly data for Japan 2003 oil...Ch. 4.2 - Prob. 2CPCh. 4.2 - Prob. 3CPCh. 4.2 - Prob. 4CPCh. 4.2 - Prob. 5CPCh. 4.2 - Prob. 6CPCh. 4.2 - Prob. 7CPCh. 4.2 - The file scrippsy. txt, available from the...Ch. 4.2 - The file scrippsm.txt, available from the textbook...Ch. 4.3 - Apply classical Gram-Schmidt orthogonalization to...Ch. 4.3 - Apply classical Gram-Schmidt orthogonalization to...Ch. 4.3 - Apply modified Gram--Schmidt orthogonalization to...Ch. 4.3 - Apply modified Gram-Schmidt orthogonalization to...Ch. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Find the QR factorization and use it to solve the...Ch. 4.3 - Prove that a square matrix is orthogonal if and...Ch. 4.3 - Prove that the product of two orthogonal mm...Ch. 4.3 - Show that the Gram-Schmidt orthogonalization of an...Ch. 4.3 - Show that the Householder reflector method for the...Ch. 4.3 - Let P be the matrix defined in (4.29). Show (a)...Ch. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.3 - Write a MATLAB program that implements the...Ch. 4.3 - Apply the classical Gram-Schmidt, modified...Ch. 4.3 - Prob. 3CPCh. 4.3 - Write a MATLAB program that implements (a)...Ch. 4.3 - Prob. 5CPCh. 4.3 - Use the MATLAB QR factorization to find the least...Ch. 4.3 - Prob. 7CPCh. 4.3 - Let x1,...,x11be11 be evenly spaced points in...Ch. 4.4 - Solve Ax=b for the following A and b=[ 1,0,0 ]T,...Ch. 4.4 - Prob. 2ECh. 4.4 - Let A=[ 10a1301a23001 ]. Prove that for any x0 and...Ch. 4.4 - Prob. 4ECh. 4.4 - Prob. 1CPCh. 4.4 - Prob. 2CPCh. 4.4 - Prob. 3CPCh. 4.4 - Let A be the matrix from Computer Problem 3, but...Ch. 4.4 - Prob. 5CPCh. 4.5 - The Gauss-Newton Method can be applied to find the...Ch. 4.5 - Prob. 2ECh. 4.5 - Prove that the distance from a point (x,y) to a...Ch. 4.5 - Prob. 4ECh. 4.5 - Find the matrix Dr needed for the application of...Ch. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Prob. 1CPCh. 4.5 - Prob. 2CPCh. 4.5 - Prob. 3CPCh. 4.5 - Prob. 4CPCh. 4.5 - Prob. 5CPCh. 4.5 - Prob. 6CPCh. 4.5 - Prob. 7CPCh. 4.5 - Prob. 8CPCh. 4.5 - Prob. 9CPCh. 4.5 - Prob. 10CPCh. 4.5 - Prob. 11CPCh. 4.5 - Prob. 1SACh. 4.5 - Prob. 2SACh. 4.5 - Prob. 3SACh. 4.5 - Prob. 4SACh. 4.5 - Now repeat Step 4 with a more tightly grouped set...Ch. 4.5 - Decide whether the GPS en-or and condition number...
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- For each of the time series, construct a line chart of the data and identify the characteristics of the time series (that is, random, stationary, trend, seasonal, or cyclical). Date IBM9/7/2010 $125.959/8/2010 $126.089/9/2010 $126.369/10/2010 $127.999/13/2010 $129.619/14/2010 $128.859/15/2010 $129.439/16/2010 $129.679/17/2010 $130.199/20/2010 $131.79 a. Construct a line chart of the closing stock prices data. Choose the correct chart below.arrow_forward1) Express these large and small numbers from the Read and Study section in scientific notation: (a) 239,000 miles (b) 3,800,000,000,000 sheets of paper (c) 0.0000000000000000000000167 grams 2) Find all values for the variable x that make these equations true. (a) 5x = 1 (b) 3x = 1/1 9 (c) 4* = 11/ 4 (e) 4* = 64 (g) 10x = 1,000,000 (d) 3x=-3 (f) 2x = = 8 (h) 10x = 0.001arrow_forward(b) 4) Find an equation to fit each of the following graphs: (a) 20 20 18 16 14 12 10 8 6 4 2 24 22 20 18 16 14 12 10 8 16 A 2 -3 -2 -1-0 2 3 4. -1 0 1 2 3. -2 -2arrow_forward
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- 5) State any theorems that you use in determining your solution. a) Suppose you are given a model with two explanatory variables such that: Yi = a +ẞ1x1 + ẞ2x2i + Ui, i = 1, 2, ... n Using partial differentiation derive expressions for the intercept and slope coefficients for the model above. [25 marks] b) A production function is specified as: Yi = α + B₁x1i + ẞ2x2i + Ui, i = 1, 2, ... n, u₁~N(0,σ²) where: y = log(output), x₁ = log(labor input), x2 = log(capital input) The results are as follows: x₁ = 10, x2 = 5, ỹ = 12, S11 = 12, S12= 8, S22 = 12, S₁y = 10, = 8, Syy = 10, S2y n = 23 (individual firms) i) Compute values for the intercept, the slope coefficients and σ². [20 marks] ii) Show that SE (B₁) = 0.102. [15 marks] iii) Test the hypotheses: ẞ1 = 1 and B2 = 0, separately at the 5% significance level. You may take without calculation that SE (a) = 0.78 and SE (B2) = 0.102 [20 marks] iv) Find a 95% confidence interval for the estimate ẞ2. [20 marks]arrow_forwardPage < 2 of 2 - ZOOM + The set of all 3 x 3 upper triangular matrices 6) Determine whether each of the following sets, together with the standard operations, is a vector space. If it is, then simply write 'Vector space'. You do not have to prove all ten vector space axioms. If it is not, then identify one of the ten vector space axioms with its number in the attached sheet that fails and also show that how it fails. a) The set of all polynomials of degree four or less. b) The set of all 2 x 2 singular matrices. c) The set {(x, y) : x ≥ 0, y is a real number}. d) C[0,1], the set of all continuous functions defined on the interval [0,1]. 7) Given u = (-2,1,1) and v = (4,2,0) are two vectors in R³-space. Find u xv and show that it is orthogonal to both u and v. 8) a) Find the equation of the least squares regression line for the data points below. (-2,0), (0,2), (2,2) b) Graph the points and the line that you found from a) on the same Cartesian coordinate plane.arrow_forward1. A consumer group claims that the mean annual consumption of cheddar cheese by a person in the United States is at most 10.3 pounds. A random sample of 100 people in the United States has a mean annual cheddar cheese consumption of 9.9 pounds. Assume the population standard deviation is 2.1 pounds. At a = 0.05, can you reject the claim? (Adapted from U.S. Department of Agriculture) State the hypotheses: Calculate the test statistic: Calculate the P-value: Conclusion (reject or fail to reject Ho): 2. The CEO of a manufacturing facility claims that the mean workday of the company's assembly line employees is less than 8.5 hours. A random sample of 25 of the company's assembly line employees has a mean workday of 8.2 hours. Assume the population standard deviation is 0.5 hour and the population is normally distributed. At a = 0.01, test the CEO's claim. State the hypotheses: Calculate the test statistic: Calculate the P-value: Conclusion (reject or fail to reject Ho): Statisticsarrow_forward
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