Find the coordinates of the vertices of each figure after the given transformation.roțațion 90° counterclockwise about theoriginO s(2, 1), T'(4, –2), U'(2, –4), v'(1, –3)O S'(1, –3), T"(-1,0), U'(1, 2), V'(2, 1)O S'(1, –2), T'(-2, –4), U'(-4, –2), V'(-3, –1)O S'(-3, –3), T"(-5,0), U'(-3,2), v'(-2, 1)489 10

Answered: Find the coordinates of the vertices of…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CM: Cumulative Review

Problem 25CM: Find a basis B for R3 such that the matrix for the linear transformation T:R3R3,...

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Similar questions

Let T:P2P3 be the linear transformation T(p)=xp. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3}.
Let T:P2P4 be the linear transformation T(p)=x2p. Find the matrix for T relative to the bases B={1,x,x2} and B={1,x,x2,x3,x4}.
Use the standard matrix for counterclockwise rotation in R2 to rotate the triangle with vertices (3,5), (5,3) and (3,0) counterclockwise 90 about the origin. Graph the triangles.
A translation in R2 is a function of the form T(x,y)=(xh,yk), where at least one of the constants h and k is nonzero. (a) Show that a translation in R2 is not a linear transformation. (b) For the translation T(x,y)=(x2,y+1), determine the images of (0,0,),(2,1), and (5,4). (c) Show that a translation in R2 has no fixed points.
Find a basis B for R3 such that the matrix for the linear transformation T:R3R3, T(x,y,z)=(2x2z,2y2z,3x3z), relative to B is diagonal.
For the linear transformation from Exercise 45, let =45 and find the preimage of v=(1,1). 45. Let T be a linear transformation from R2 into R2 such that T(x,y)=(xcosysin,xsin+ycos). Find a T(4,4) for =45, b T(4,4) for =30, and c T(5,0) for =120.
Find the centralizer for each element a in each of the following groups. The quaternion group G={ 1,i,j,k,1,i,j,k } in Exercise 34 of section 3.1 (Sec. 3.1, #34). G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of section 3.1 (Sec. 3.1, #36). G={ I3,P1,P2,P3,P4,P5 } in Exercise 35 of section 3.1 (Sec. 3.1, #35). Sec. 3.1,34 34. Let G be the set of eight elements G={ 1,i,j,k,1,i,j,k } with identity element 1 and noncommutative multiplication given by (1)2=1, i2=j2=k2=1, ij=ji=k jk=kj=i, ki=ik=j, x=(1)x=x(1) for all x in G (The circular order of multiplication is indicated by the diagram in Figure 3.8.) Given that G is a group of order 8, write out the multiplication table for G. This group is known as the quaternion group. (Sec. 3.3,22a,32a, Sec. 3.4,2, Sec. 3.5,11, Sec. 4.2,8, Sec. 4.4,23, Sec. 4.5,40a, Sec. 4.6,3,11,16) Sec. 3.1,36 Consider the matrices R=[ 0110 ] H=[ 1001 ] V=[ 1001 ] D=[ 0110 ] T=[ 0110 ] in GL(2,), and let G={ I2,R,R2,R3,H,D,V,T }. Given that G is a group of order 8 with respect to multiplication, write out a multiplication table for G. (Sec. 3.3,22b,32b, Sec. 4.1,22, Sec. 4.6,14) Sec. 3.1,35 35. A permutation matrix is a matrix that can be obtained from an identity matrix In by interchanging the rows one or more times (that is, by permuting the rows). For n=3 the permutation matrices are I3 and the five matrices. (Sec. 3.3,22c,32c, Sec. 3.4,5, Sec. 4.2,6) P1=[ 100001010 ] P2=[ 010100001 ] P3=[ 010001100 ] P4=[ 001010100 ] P5=[ 001100010 ] Given that G={ I3,P1,P2,P3,P4,P5 } is a group of order 6 with respect to matrix multiplication, write out a multiplication table for G.
Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
Let T be a linear transformation from R2 into R2 such that T(x,y)=(xcosysin,xsin+ycos). Find a T(4,4) for =45, b T(4,4) for =30, and c T(5,0) for =120.
22. Find the center for each of the following groups . a. in Exercise 34 of section 3.1. b. in Exercise 36 of section 3.1. c. in Exercise 35 of section 3.1. d., the general linear group of order over. Exercise 34 of section 3.1. Let be the set of eight elements with identity element and noncommutative multiplication given by for all in (The circular order of multiplication is indicated by the diagram in Figure .) Given that is a group of order , write out the multiplication table for . This group is known as the quaternion group. Exercise 36 of section 3.1 Consider the matrices in , and let . Given that is a group of order 8 with respect to multiplication, write out a multiplication table for. Exercise 35 of section 3.1. A permutation matrix is a matrix that can be obtained from an identity matrix by interchanging the rows one or more times (that is, by permuting the rows). For the permutation matrices are and the five matrices. Given that is a group of order with respect to matrix multiplication, write out a multiplication table for .
For the linear transformation from Exercise 38, find a T(0,1,0,1,0), and b the preimage of (0,0,0), c the preimage of (1,1,2). Linear Transformation Given by a Matrix In Exercises 33-38, define the linear transformation T:RnRmby T(v)=Av. Find the dimensions of Rnand Rm. A=[020201010112221]

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