5. Triangularisation with an orthogonal matrix Example 7.9 in the Study Guide (pages 21-23 of Topic...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
5. Triangularisation with an orthogonal matrix Example 7.9 in the Study Guide (pages 21-23 of Topic 7) shows the triangularisation procedure for a matrix. Consider the following matrix A, which also has eigenvalues 1, 1 and 5. A = . 3 2 1 -1 R = - 2 2 -1 i. Construct a matrix S such that it is an orthogonal matrix with the first column corresponding with the eigenvector 0 A Calculate S-¹ AS. ii. Show that for the resulting matrix, S-¹ AS = -1 2 [ A] 1 b 1 and 5 by determining and then simplifying its characteristic equation. 2 the 2 x 2 matrix A₁ has eigenvalues iii. Find the eigenvector from A₁ corresponding with λ = 1 and then construct an orthogonal 2 x 2 matrix Q where the first column is based on your eigenvector. Hence construct the matrix 1 00 [ 0 Q iv. Calculate P = SR. Show that P is an orthogonal matrix and verify that P-¹AP is upper triangular. 5 marks 5. Triangularisation with an orthogonal matrix Example 7.9 in the Study Guide (pages 21-23 of Topic 7) shows the triangularisation procedure for a matrix. Consider the following matrix A, which also has eigenvalues 1, 1 and 5. A = . 3 2 1 -1 R = - 2 2 -1 i. Construct a matrix S such that it is an orthogonal matrix with the first column corresponding with the eigenvector 0 A Calculate S-¹ AS. ii. Show that for the resulting matrix, S-¹ AS = -1 2 [ A] 1 b 1 and 5 by determining and then simplifying its characteristic equation. 2 the 2 x 2 matrix A₁ has eigenvalues iii. Find the eigenvector from A₁ corresponding with λ = 1 and then construct an orthogonal 2 x 2 matrix Q where the first column is based on your eigenvector. Hence construct the matrix 1 00 [ 0 Q iv. Calculate P = SR. Show that P is an orthogonal matrix and verify that P-¹AP is upper triangular. 5 marks
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
There are certain instances where pooling of operations can be desirable. For example, a large factory may have two or more locations where mechanics can obtain special tools or equipment they...
-
1. More than 13 million people are admitted to American jails each year. Albert Florence was mistakenly arrested and subjected to two strip searches involving showering with a delousing agent,...
-
Piercing the corporate veil is a very difficult argument to win and courts usually warranted in extraordinary circumstances. Why do you think that is so?
-
In Exercises explain why Rolle's Theorem does not apply to the function even though there exist a and b such that (a) = (b). f(x) H [1,1]
-
State the four conditions of a binomial experiment. Give one example of such an experiment.
-
Describe a procedure for finding the inverse of a square matrix.
-
Furniture Depot is a retail chain selling furniture and appliances. The firm has after-tax operating income of \($250\) million in the current year on revenues of \($5\) billion. The firm also has...
-
The following items are from Taperline Corporation on December 31, 2010. Assume a flat 40% corporate tax rate on all items, including the casualty loss. Sales .................. $670,000 Rental...
-
The price of a European call and put on a stock are $2 and $5, respectively. Both have a strike price of $45 and an expiration date of 6 months. The current price of the underlying nondividend-...
-
Westley Fong, manager of The Lucky 88 Motel, has a contract with Appraisers Associates to appraise his 150-room motel, which is located in beautiful downtown Wahiawa. The consultant on the job has...
-
Problem 2: Standard Costing Morton Company's budgeted variable manufacturing overhead is $4.50 per direct labor-hour and its budgeted fixed manufacturing overhead is $270,000 per year. The company...
-
Subtract and simplify. (6-7i)-(-3+i)
-
Task 2: Comparison and Classification (6 marks): (a) How do different comparison techniques affect linkage results? Discuss and justify how you selected appropriate com- parison functions for...
-
SPY Call Option Data, exercise date 5/2/2022 Contract Name Strike Last Price Volume Open Interest Implied Volatility SPY220502C00355000 355 103.82 - 1 0.682 SPY220502C00360000 360 83.3 2 2 0.6462...
-
The premise of the experiment is: In a group of 10 people, present your findings with different mathematical models (eg, logistics, SI, SIS) or any other mathematical models. An initial person has a...
-
Social Media Marketing is much more than simply throwing up a website. Identify what you believe will be the three greatest challenges of developing your personal brand online. State why for each one?
-
COTB MC Qu. 1-84 (Algo) Assume that a manufacturing company incurred... Assume that a manufacturing company incurred the following costs: Direct labor $ 90,000 Advertising $ 40,000 Factory supervisi...
-
Cornell and Roberts are partners who agree to admit Stanley to their partnership. Cornell has a capital balance of $80,000 and Roberts has a capital balance of $120,000. Cornell and Roberts share net...
-
Given the following table, construct a network diagram, either AOA or AON. Times are in days. a. Determine the expected duration of the project. b. Compute the probability that the project will take...
-
Arrange six departments into a 2 3 grid so that these conditions are satisfied: 1 close to 2, 5 close to 2 and 6, 2 close to 5, and 3 not close to 1 or 2.
-
Respond to this statement: The importance of the location decision is often vastly overrated; the fact that virtually every type of business is located in every section of the country means there...
-
\(7 \sqrt{5}+6 \sqrt{14}\) Perform the arithmetic operations without a calculator, if possible. If it is not possible, state why.
-
\(7.3 \sqrt{45}-6.8 \sqrt{20}\) Perform the arithmetic operations without a calculator, if possible. If it is not possible, state why.
-
\(19.8 \sqrt{12}-6.1 \sqrt{3}\) Perform the arithmetic operations without a calculator, if possible. If it is not possible, state why.
Study smarter with the SolutionInn App