Question: T: R2 R2 is the rotation about the origin through 45°; B and B² are the bases in Exercise 1. Find the matrix of T

T: R2 †’ R2 is the rotation about the origin through 45°; B and B€² are the bases in Exercise 1.
Find the matrix of T with respect to the basis B, and use Theorem 8.5.2 to compute the matrix of T with respect to the basis B€².
Exercise 1
T: R2 †’ R2 is defined by

B= {u1, u2} and B€² = {v1, v2}, where

X1 A2 4 1 0 2 10

Step by Step Solution

★★★★★

3.39 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Since Tu 1 12 12 and Tu 2 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

938-M-L-A-E (1417).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Find the matrix of T with respect to the basis B, and use Theorem 8.5.2 to compute the matrix of T with respect to the basis B². T: R2 R2 is defined by B= {u1, u2} and B² = {v1, v2}, where...

T: R3 R3 is the orthogonal projection on the x,y-plane; B and B² are as in Exercise 4. Find the matrix of T with respect to the basis B, and use Theorem 8.5.2 to compute the matrix of T with...

Let And let be the matrix for T: R2 R2 with respect to the basis B = (v1, v2). (a) Find [T(v1)]B and [T(v2)]B. (b) Find T(v1) and T(v2). (c) Find a formula for (d) Use the formula obtained in (c) to...

THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF MATHEMATICS AND STATISTICS JUNE 2015 MATH2501 Linear Algebra (1) TIME ALLOWED - THREE HOURS. (2) TOTAL NUMBER OF QUESTIONS - 5 (3) ANSWER ALL QUESTIONS (4)...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

5.1 please only write on paper. no explanation needed. Questions: 1,3,5,7,9, 25 on paper 5.1 Eigenvalues and Eigenvectors 299 Exercise Set 5.1 In Exercises 1-4, confirm by multiplication that x is an...

8.4 Write on paper for upvote please. Questions: 12, 17, 22 8.4 Matrices for General Linear Transformations 485 b. Verify that Formula (8) holds for every vector in R'. d. Use the formula obtained in...

Math 21 Winter 2017 Professor Bruce Cooperstein Final Review/Practice Examination You will need to know the definitions of the following in order to do the questions on the examination. You will not...

linear algebra 5.8 MATLAB: Change of Bases LAB ACTIVITY 5.8.1: MATLAB: Change of Bases This tool is provided by a third party. Though your activity may be recorded, a page refresh may be needed to...

Find a basis for the eigenspace corresponding to the eigenvalue. - 12 J A = 14 ,2=3 3 -39 A basis for the eigenspace corresponding to 2 = 3 is {} (Type a vector or list of vectors. Type an integer or...

A sociologist claims that the age distribution for the residents of a city is different from the distribution 10 years ago. The distribution of ages 10 years ago is shown in the table at the left....

Suppose that X1 and X2 have a bivariate normal distribution for which E(X1|X2) = 3.7 0.15X2, E(X2|X1) = 0.4 0.6X1, andVar(X2|X1) = 3.64. Find the mean and the variance of X1, the mean and the...

Andrea is buying a house for $ 2 0 0 , 0 0 0 she plans to make a 1 2 % down payment closing cost include $ 8 5 0 for six months of homeowners insurance $ 7 0 0 for six months of property tax $ 1 5 0...

7. The sovereign debt crisis in the Eurozone attracted large capital inflows to Switzerland. As a result, from 2009 to 2015 the value of the Swiss franc surged dramatically relative to the euro. a....

Show that the eigen values of a triangular matrix are the diagonal elements of the matrix.

Let Q be 3 x 3 orthogonal matrix whose determinant is equal to 1. (a) If the eigenvalues of Q are all real and if they an' ordered so that 1 2 3. deternine values of all possible triples of...

Let x1 .... xr be eigenvectors of an n x n matrix A and let S be the ssubspace of R spanned by x1. x2 ....xf Show that S is invariant under A (i.e.. show that Ax S whenever x 5).

You find the following corporate bond quotes. To calculate the number of years until maturity, assume that it is currently January 15, 2016. The bonds have a par value of $2,000. Company (Ticker)...

(1) In the International Baccalaureate (LB) programs of high schools, during the senior year 45% of students study subject A, 40% study subject B, and 50% study subject C. It is also known that 20%...

Stat question QUESTION 18 The above research scenario had a relatively small sample size of 20 individuals per group (and thus a total sample of 40 individuals). A second research team comes along...