QUESTION 18Use the standard matris for the lincar transformation T. +' defincl by Tx,3)- (4-6y, 5x+2y,y) to find the image of the vector - (2,-2).O. 12, -2) --4, 14, 2)O . 72, -2) - (6, -2, 20)O. 12, -2) - (18, 16, 2)Od. 72, -2) - (14, 20, 10)O. 12, -2)-20, 6, -2)QUESTION 19Find the coordinate matrix of P- 2-15r-3 relative to the standand hasis in P22o bls- -16-33O bl- 162O bl; - 16-3Od. lels- -162O. ely - 16QUESTION 20Find a hasis for and the dimension of the solution space of Ax -01 225 13 7393o. (4, 1, 0). (0, 0, 1), dim -3O t. {(-4, 1, 0)), dim -O. (4, 1, 0). (0, 0, 1)), dim -2Od. {(4, 1, 1)), dim -O. {(-4, 1, 1), dim - 1

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Answered: Use the staralard matris Sor the lincur…

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Use the staralard matris Sor the lincur Iransformaticn 2: defincil by 2X, firal the imae of the vector T-

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 6CM: Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a...

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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.
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***PLEASE HELP WITH THE FOLLOWING AND PLEASE PROVIDE HANDWRITTEN WORK ON PAPER*** (6) Let T R3 --> R3 be a linear transformation such that T(1,1,1) = (2,0,-1), T(0,-1,2) = (-3,2,-1) and T (1,0,1) = (1,1,0) find T (2, -1,1)