I The linear transformation T: R R. T(2) Ar, is defined by the matrix A relative...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
I The linear transformation T: R³ R³. T(2) Ar, is defined by the matrix A relative to the standard basis B={₁,2,3}: [102] A=0 3 0 - 201 4. Show that D = PT AP = 8. 1. Find the eigenvalues (₁) for A. 2. Find the set of orthornormal eigenvectors {p}. 3. Show that the P = P₁ P2 P3] is symmetric, i.e. PT = P-1 A₁ 0 0 0 1₂ 0. 0 0 5. Bonus. Show that pi Api = X₁ €2 = B -8. 6. D is the matrix for T with respect to the eigenbasis B'={p.P2, P3). i. Is P from 3. the transition matrix from B' to B? Hint: Does [B' B] → [I P-1] produce the same P? III Find the orthogonal compliment to S 23 = ii. What do each of the eigenvectors look like with respect to the eigenbasis? Hint: P = P¹PB. II Using the vectors =(-1,0,1) and = (0, 1.0) solve the following problems 1. 5-40 5. x 2. d(50, 40) 6. 3. (5)-(40) 4. proje 7. span{ x+x (-proj #) WMAT-291, section W1, xbhcc moodle - Bing X 2021SP MAT-291-W1: X ← > C Ⓒ File | C:/Users/youssef/Downloads/MAT291_Final_SP21.pdf 2 A of 2 Q Type here to search + (0) IV The matrix A = A = Find the kernal and range (row space) of T. O Using A= PDF V Using any method covered this semester, solve the system Az= b using the following matrices: 1 0 5 0 6= 8 -2 1 4 < A, B >= aobo + aıbı +2a2b2 +3a3b3. 1 0 -2 0 5 0 defines the linear transformation T:R³ → R³, T(7) = Az. -2 1 4 VI An inner product for M2,2 matrices {4=[90], ao, a1, 02, 03 € R} is defined as 02 03 2 [13] CD Page view A Read aloud | Draw MAT291_Final_SP21.pc X 6: and B= 3. Calculate || B||. 4. Calculate < A,B>. 1. Calculate the determinant [2B³|. 2. Calculate ||A|| = √√<A,A>. course hero - Bing answer the following questions. 5. Calculate the angle between A and B. 6. List one isomorphic vector space to M₂,2- V X Course Hero Highlight Q x + Erase 0 [+] A P 60 x 4x J 10 12:09 PM 5/16/2021 I The linear transformation T: R³ R³. T(2) Ar, is defined by the matrix A relative to the standard basis B={₁,2,3}: [102] A=0 3 0 - 201 4. Show that D = PT AP = 8. 1. Find the eigenvalues (₁) for A. 2. Find the set of orthornormal eigenvectors {p}. 3. Show that the P = P₁ P2 P3] is symmetric, i.e. PT = P-1 A₁ 0 0 0 1₂ 0. 0 0 5. Bonus. Show that pi Api = X₁ €2 = B -8. 6. D is the matrix for T with respect to the eigenbasis B'={p.P2, P3). i. Is P from 3. the transition matrix from B' to B? Hint: Does [B' B] → [I P-1] produce the same P? III Find the orthogonal compliment to S 23 = ii. What do each of the eigenvectors look like with respect to the eigenbasis? Hint: P = P¹PB. II Using the vectors =(-1,0,1) and = (0, 1.0) solve the following problems 1. 5-40 5. x 2. d(50, 40) 6. 3. (5)-(40) 4. proje 7. span{ x+x (-proj #) WMAT-291, section W1, xbhcc moodle - Bing X 2021SP MAT-291-W1: X ← > C Ⓒ File | C:/Users/youssef/Downloads/MAT291_Final_SP21.pdf 2 A of 2 Q Type here to search + (0) IV The matrix A = A = Find the kernal and range (row space) of T. O Using A= PDF V Using any method covered this semester, solve the system Az= b using the following matrices: 1 0 5 0 6= 8 -2 1 4 < A, B >= aobo + aıbı +2a2b2 +3a3b3. 1 0 -2 0 5 0 defines the linear transformation T:R³ → R³, T(7) = Az. -2 1 4 VI An inner product for M2,2 matrices {4=[90], ao, a1, 02, 03 € R} is defined as 02 03 2 [13] CD Page view A Read aloud | Draw MAT291_Final_SP21.pc X 6: and B= 3. Calculate || B||. 4. Calculate < A,B>. 1. Calculate the determinant [2B³|. 2. Calculate ||A|| = √√<A,A>. course hero - Bing answer the following questions. 5. Calculate the angle between A and B. 6. List one isomorphic vector space to M₂,2- V X Course Hero Highlight Q x + Erase 0 [+] A P 60 x 4x J 10 12:09 PM 5/16/2021
Expert Answer:
Answer rating: 100% (QA)
Sure lets provide the correct answers to each part of the given question 1 Eigenvalues for A The giv... View the full answer
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
Find the standard matrix of the linear transformation T : R2 R2 that corresponds to a counterclockwise rotation of 45o about the origin followed by a projection onto the line y = -2x
-
In Exercises 1-3, determine whether the linear transformation T is (a) one-to-one and (b) onto. 1. T: R2 R2 defined by 2. T: R2 P2 defined by = (a-2b) + (3a + b)x + (a + b)X2
-
In Exercises 1-3, determine whether the linear transformation T is invertible by considering its matrix with respect to the standard bases. If T is invertible, use Theorem 6.28 and the method of...
-
Information sent electronically over the Internet affords little privacy. One of the reasons that cryptography is included in this text is because its importance is growing due to the increasing need...
-
The letter to the shareholders from Douglas N. Daft, Chairman, Board of Directors, and Chief Executive Officer of Coca-Cola is provided on the texts Web site and on the student CD that accompanies...
-
A spherical bowling ball with mass m = 3.7 kg and radius R = 0.102 m is thrown down the lane with an initial speed of v = 8.8 m/s. The coefficient of kinetic friction between the sliding ball and the...
-
During a flash flood, water rushes over a road as shown in Fig. P9. 67 with a speed of \(12 \mathrm{mph}\). Estimate the maximum water depth, \(h\), that would allow a car to pass without being swept...
-
Water Sport Inc. manufactures a small personal water tube used for children learning to swim. Management is now preparing detailed budgets for the third quarter, July through September, and has...
-
Explain how the selection of absorbents with specific chemical functionalities can enhance selectivity and capacity in applications such as carbon capture and ammonia scrubbing. What are the key...
-
A sample of 20 items provides a sample standard deviation of 5. a. Compute the 90% confidence interval estimate of the population variance. b. Compute the 95% confidence interval estimate of the...
-
2. Consider this recurrence: T(n) Solution: = 4T(n/3)+2n when n > 1, when n = 1. (a) How many levels will the recurrence tree have? (b) What is the cost at the level below the root? (c) What is the...
-
Write ME if the given is a plain mathematical expression and write MS if it is a mathematical sentence. (1 point each) 1. x + y 5 2. [a, b] 1. 2. 3. 4. 5. 3. V = rh + 4. MMXX 5.32 Z such that 22 16...
-
You are an employee of the human resources division of a major Canadian company. You have been assigned the task of designing a workplace policy (the business does not currently have a policy) that...
-
3. Marie was employed by Rigney Construction as a bookkeeper and office manager for over 10 years. Without notice or explanation, Rigney informed Marie that her services were no longer required and...
-
Ali offered to purchase Sams pool for $400 cash. Ali and sam agreed that sam would deliver the pool to Alis house on march 1, at which time Ali would pay the $400. On march 1, when sam did not...
-
Buyer, who has never owned a computer, goes to Merchant Seller and buys a used computer for $4,000. Buyer is not pressured to purchase this computer, but Buyer does no research and does not price...
-
Buildz Manufacturing is currently producing 2.000 monthly charts. Data per unit below The tables apply to sales to regular customers: Direct materials $5 Direct manufacturing labor 12 Variable...
-
If there is an unrealized holding gain on available-for-sale investments, it is reported as?
-
State which of the following is an example of sampling with replacement and which is an example of sampling without replacement. a. Selecting 10 patients out of 100 to test a new drug b. Selecting...
-
Standard milk chocolate M& come in six colors. The Fun Size bags typically contain between 16 and 20 candies, so it is common for a Fun Size bag to have some of the six colors missing. Each of the 14...
-
Refer to Exercise 10.28. Now assume that the two populations are normally distributed with unequal and unknown population standard deviations. In Exercise 28 a. Make a 90% confidence interval for the...
-
Use the internet to identify all the infrastructure projects currently taking place in your local area. How many are you able to find? What is the value of the projects? How long are they planned to...
-
Review the PMI site (www.pmi.org). (a) Review general information about the PMI, as well as membership information. (b) See if there is a PMI chapter in your state. If not, where is the closest one?...
-
Individually identify a recent project. Are both socio-cultural and technical elements factors in the success or difficulties in the projects?
Study smarter with the SolutionInn App