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For Problems 1-7, determine whether the given set
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- 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 .arrow_forwardHere you have to show that for the given A and B matrix in the question (AB)-1 = B-1 A-1arrow_forwardIf Ax = Bx for some nonzero vector x, then the matrices A and B must be equal.arrow_forward
- deal with the problem of solving Ax = b when det A = 0.22.Suppose that, for a given matrix A, there is a nonzero vector x such that Ax = 0. Show that there is also a nonzero vector y such that A*y = 0.arrow_forwardin number 1, B is the matrix representation of Z with respect to B only, not B and B'. The formula won't work for that, will it?arrow_forwardFor parts: a,b,c,d,e Job Title Salary Large Company US Employer Remote Data Science Consultant 64369 1 0 1 Head of Data Science 85000 0 0 0 Head of Data 230000 1 0 1 Machine Learning Engineer 125000 0 1 1 Data Analytics Manager 120000 0 1 1 Data Science Engineer 127543 1 0 1 Manager Data Science 144000 1 1 1 Data Scientist 13400 1 0 1 Data Scientist 75966 1 0 1 Data Scientist 150000 0 1 1 Data Engineering Manager 153000 1 1 1 Data Engineer 90000 1 1 1 Data Analyst 90000 0 1 1 Data Analyst 60000 0 1 1 Data Scientist 50000 1 0 1 Applied Data Scientist 54376 1 0 1 Machine Learning Engineer 47681 0 0 1 Director of Data Science 154963 1 0 1 Data Engineer 28801 1 0 1 Data Analytics Engineer 110000 1 1 1 Research Scientist 83000 1 0…arrow_forward
- This question is regarding vectors and matrices, what do I match these 4 parts with when the 5 choices to match with are: It equals 1 It is meaningless It equals 0 It equals 4 It equals the zero vectorarrow_forwardSolve the following four task about the matrix A where C1, C2, …, C5 denote its columns: (a). Find a basis of the RS(A) (b). Find each column Ck of A that is a linear combination of preceding columns of A. (c). Find a basis of the column space of A. (d). Find the rank of A.arrow_forwardIn Problems 2 to 4, find out whether the given vectors are dependent or independent; if they are dependent, find a linearly independent subset. Write each of the given vectors as a linear combination of the independent vectors.2. (1, −2, 3), (1, 1, 1), (−2, 1, −4), (3, 0, 5) 3. (0, 1, 1), (−1, 5, 3), (1, 0, 2), (2, −15, 1)4. (3, 5, −1), (1, 4, 2), (−1, 0, 5), (6, 14, 5)arrow_forward
- Find the solution to the following [] means its a matrix and ^ above y is vector yarrow_forwardFor each of the following, factor the given matrix into a product LDLT, where L is lower triangular with 1’s on the diagonal and D is a diagonal matrix:arrow_forwardIf A is m by n, how many separate multiplications are involved when(a) A multiplies a vector x with n components?(b) A multiplies an n by p matrix B?( c) A multiplies itself to produce A2 ? Here m = n.arrow_forward
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