(Application of LU factorization): When computing the determinant of a matrix by hand, it is common...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
(Application of LU factorization): When computing the determinant of a matrix by hand, it is common to use cofactor expansion and apply the definition recursively. But this is terribly inefficient as a function of the matrix size. (a) (By Hand) Explain why, if A = LU is an LU factorization, where uii, li, i=1,2,.. TL det (A) = u₁1¹₁1¹22l22 ··· Unnlnn = [¹, i=1 ,n are the diagonal elements of U and L respectively. (b) (By Matlab)Using the result of part (a), write a MATLAB function determinant that computes the determinant of a given matrix A using mylu from lecture. Include the function at the end of your live script. Display the determinant of the matrices magic(n) for n = 3,4, ..., 7 by using your function built in (b) and the Matlab built-in function det. (Application of LU factorization): When computing the determinant of a matrix by hand, it is common to use cofactor expansion and apply the definition recursively. But this is terribly inefficient as a function of the matrix size. (a) (By Hand) Explain why, if A = LU is an LU factorization, where uii, li, i=1,2,.. TL det (A) = u₁1¹₁1¹22l22 ··· Unnlnn = [¹, i=1 ,n are the diagonal elements of U and L respectively. (b) (By Matlab)Using the result of part (a), write a MATLAB function determinant that computes the determinant of a given matrix A using mylu from lecture. Include the function at the end of your live script. Display the determinant of the matrices magic(n) for n = 3,4, ..., 7 by using your function built in (b) and the Matlab built-in function det.
Expert Answer:
Answer rating: 100% (QA)
a If ALU is an LU factorization of A where L is a lower triangular matrix with ones on the diagonal ... View the full answer
Related Book For
Differential Equations and Linear Algebra
ISBN: 978-0131860612
2nd edition
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
Posted Date:
Students also viewed these programming questions
-
Why does required returns (as calculated by the CAPM) not always coincide with realized returns? Markets are inefficient Beta is estimated not observed Constructing the true market portfolio is...
-
It is common to use rotation-inversion axes (rather than rotation-reflection axes) to classify the symmetry of crystals. Any Sn axis is equivalent to a rotation-inversion axis (symbolized by p) whose...
-
An elevator has a maximum capacity of 2500 lb When rating elevators, it is common to use a 25 safety factor, so the elevator should actually be able to carry a load that is 25 greater than the stated...
-
A strange function. Consider McCarthys 91 function: public static int mcCarthy(int n) { if (n > 100) return n - 10; return mcCarthy(mcCarthy(n+11)); } Determine the value of mcCarthy(50) without...
-
For the configuration shown in Figure P24.57, suppose that a = 5.00 cm, b = 20.0 cm, and c = 25.0 cm. Furthermore, suppose that the electric field at a point 10.0 cm from the center is measured to be...
-
An observer in the laboratory finds that an electron's total energy is 5.0mc2. What is the magnitude of the electron's momentum (as a multiple of mc), as observed in the laboratory?
-
An airline claims that only \(6 \%\) of all lost luggage is never found. If, in a random sample, 17 of 200 pieces of lost luggage are not found, test the null hypothesis \(p=0.06\) against the...
-
Lower of Cost or Market Frost Companys inventory records for the years 2016 and 2017 reveal the cost and market of the January 1, 2016, inventory to be $125,000. On December 31, 2016, the cast of...
-
Consider a spherical bacterium, with radius 1.4 m , falling in water at 20 C. Find the terminal speed of the spherical bacterium in meters per second, ignoring the buoyant force on the bacterium and...
-
Market Corporation owns 100% of Subsidiary Corporation's stock. Market Corporation completely liquidates Subsidiary Corporation, receiving land with a $400,000 adjusted basis and a $500,000 FMV in...
-
IP Addresses: (2 points) PC-A IP address is 192.168.10.140/25 PC-B IP address is 172.16.30.99/27 Central G0/0/0 uses the last host IP of the subnet. Central G0/0/1 uses the first host IP of the...
-
1. Use this table to calculate (show your work for partial credit) A. Currency in circulation 2,100 B. Money market mutual fund 1,100 C. Savings account deposits (Other liquid deposits) 13,200 D....
-
You are in the process of obtaining long-term financing for a Toronto project and evaluating different financing scenarios. How do you calculate the total interest payable on a mortgage?
-
$] 3 -1 2 then find c- A-(the inverse of B), d-(transpose of AjxB, and e-(the inverse of Alx(c-d). Put: at the end of each formula for c.d. and e in the MATLAB code. For each of the results (c.d.e),...
-
What sddctea document provides the guidance on how to properly tiedown vehicles and equipment for rail loading and movement?
-
On July 1, 2023, SeeWee Company declared a cash dividend of $5,500 to common shareholders of record on the company's books as of July 31. The dividend was paid on August 14. What is included in the...
-
A cyclist is riding with a speed of 27 km/hr. As he approaches a circular turn on the road of radius 80 m, he applies brakes and reduces his speed at a constant rate of 0.5 ms-2. What is the...
-
Don Griffin worked as an accountant at a local accounting firm for five years after graduating from university. Recently, he opened his own accounting practice, which he operates as a corporation....
-
A tank initially contains 200 gallons of fresh water but then a salt solution of unknown concentration is poured into the tank at 2 gal / min. The well-stirred mixture flows out of the tank at the...
-
Lengths Show that the distance between the heads of any two vectors uÌ and vÌ, as shown in Fig. 3 . 1 .5, has length ||uÌ - vÌ ||. Ce FIGURE 3.1.5 Diagram for Problem 82
-
Long-Term Behavior of Solutions: Suppose that r1 and r2 are the characteristic roots for ay" + by' + cy = 0, so the solution is y(t) = c1er1t. For Problems 1-2, discuss the long-term solution...
-
If two countries had identical term structures of interest rates, what is the expected future exchange rate change between the two currencies?
-
Pick three developing countries and create a country risk index for them. Rank them ordinally in terms of factors that you can observe (exports, GDP growth, reserves, etc.) by looking at...
-
Give examples of policies that a country could implement to reduce its absorption.
Study smarter with the SolutionInn App