[0.13 0.41 0.25 0.92 0.61 0.06] 0.20 0.90 0.03 0.74 0.78 0.40 0.99 0.01 |0.70 0.73 0.29 0.88 0.93 0.02 j0.94 0.51 0.54 0.20 0.58 0.21 0.66 0.30 0.70 0.51 0.48 0.60 0.97 0.92 0.44 0.75 LA = 0.87 0.15 0.20 0.61 0.72 0.96 0.60 0.65 0.83 0.46 0.85 0.68 L0.86 0.54 0.13 0.68 0.58 0.71 B 0.71 0.45 0.71 0.71 0.49 0.36 0.06 0.88 1.00 0.67 0.66 0.58 L0.74 0.17 0.81 0.60 0.58 0.35 r0 64 011 0.66 0.04. 063 0631

11. Find two nonzero matrices and such that.

Solve for x,y and z in the matrix equation 4xyz-1=2yz-x1+24x5-x.

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 Find the center Z(G) for each of the following groups G. b. G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of section 3.1. Find the centralizer for each element a in each of the following groups. b. G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of section 3.1 Sec. 4.1,22 22. Find an isomorphism from the octic group D4 in Example 12 of this section to the group G={ I2,R,R2,R3,H,D,V,T } in Exercise 36 of Section 3.1. Sec. 4.6,14 14. Let G={ I2,R,R2,R3,H,D,V,T } be the multiplicative group of matrices in Exercise 36 of section 3.1, let G={ 1,1 } under multiplication, and define :GG by ([ abcd ])=adbc. Assume that is an epimorphism, and find the elements of K= ker . Write out the distinct elements of G/K. Let :G/KG be the isomorphism described in the proof of Theorem 4.27, and write out the values of .