1 Given that A is transformed into U by the elementary row operations below, complete E✓ ¹ and Е¹. A = -6 18 0 1 -6 1 -9 -6 1 -2R1+R3→R.3 3R₁+R₂ R2 22 18 0 22 0 -12 2 -12 0 0 6 0 30 -9 -5 = U 6 1 Ex: 42 = 1 - 1 Ez¹ 1 1 1 15
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- Let V4 stand for the Klein 4-group, which is represented by the notation V4 = a, b, c, where a = (1 2)(3 4), b = (1 3)(2 4) and c = (1 4)(2 3) (permutations of four points). Find V4 of order 2's three unique subgroups, H1, H2, and H3. Demonstrate that V4 = HiHj for all I and j and Hi Hj = 1 for all i%= j.[Note that I am referring to the Klein 4-group using the more common notation V4 rather than the less popular K4 from MT4003. V stands for Viergruppe in this case.]PYTHON /JUPYTER NOTEBOOKS Compute the rank of the stoichiometric matrix for the reaction sequence using your own algorithm. Is the matrix full rank? Is mass conserved? Explain. [[ 1. -2. 0. 0. 0. 0. 0. 0. 0.] [-1. 1. -1. 1. 1. 0. 0. 0. 0.] [ 0. 0. 1. -1. -1. 1. 1. 0. 0.] [ 0. 0. 0. -1. 0. 1. 0. 1. 0.] [ 0. -1. 0. 1. 1. 1. 0. 0. -1.]] # Pyrolysis of acetaldehyde sensitized by iodine I2 <=> 2 I I + CH3CHO <=> HI + CH3CO CH3CO <=> CH3 + CO CH3 + I2 <=> CH3I + I CH3 + HI <=> CH4 + IConstruct the branching diagram of comparisons for Binary search #2 as shown in P.151. Assume n=4 in this problem.
- Let V4 denote the Klein 4-group: that is V4 = {1, a, b, c} where a = (1 2)(3 4), b = (1 3)(2 4)and c = (1 4)(2 3) (permutations of four points). Find three distinct subgroups H1, H2and H3 of V4 of order 2. Show that Hi ∩ Hj = 1 for all i %= j and V4 = HiHj for alli and j.[Note that I am using the more conventional notation V4 for the Klein 4-group, ratherthan the less frequently used K4 from MT4003. Here V stands for Viergruppe.]The longest regular seriesIf we are provided two strings, we must identify the longest subsequence that is shared by both of them. ExampleLCS for input Sequences “ABCDGH” and “AEDFHR” is “ADH” of length 3.LCS for input Sequences “AGGTAB” and “GXTXAYB” is “GTAB” of length 4.Computer Science p=317, q=811 (a) Consider the multiplicative group F∗p and find a generator (primitive root) of it. Hint: F∗p has ϕ(p) = p − 1 elements and the order of an element must divide the order of group. (b) Use the extended Euclidean Algorithm to compute the inverse of 5 mod p
- Algorithm for B-ssgs using HomomorphismInput: soluble permutation groups G and H;a base B for G;a homomorphism f : G ----> H;a prime-step gs [g 1 ,g 2 ..... gt] of ker (f) ;a prime-step gs [f (h t) ,f (h2) ..... f (hr) ] of im (f) ;Output: a B-ssgs of G;Algorithm for a p-Central group's SeriesInput: a permutation p-group G with a base B; a prime-step B-ssgs [g 1, g 2..... gm] of G; Output: a prime-step B-ssgs [g 1, g 2..... gin] of G with a central series5. A(n) ---------------- G is a set of elements with a binary operation, denoted by *, that associates to each ordered pair (a,b) of elements in G an elements in G an element (a*b) in G. 7. we use a cubic equation in which the variables and coefficients all take on values in the set of integers from 0 through p - 1 and in which calculations are performed modulo p for a ------------------ over Zp. 8. A ----------- GF(2m) consists of 2m elements together with addition and multiplication operations that can be defined over polynomials.
- , the triple DES computation is considered here.Given three keys:K1 = 0x260b152f31b51c68K2 = 0x321f0d61a773b558K3 = 0x519b7331bf104ce3and the plaintext P = 0x403da8a295d3fed9The 16-round keys corresponding to each given key K1, K2 and K3 are compute?Round K1 K2 K31 000ced9158c9 5a1ec4b60e98 03e4ee7c63c82 588490792e94 710c318334c6 8486dd46ac653 54882eb9409b c5a8b4ec83a5 575a226a8ddc4 a2a006077207 96a696124ecf aab9e009d59b5 280e26b621e4 7e16225e9191 98664f4f54216 e03038a08bc7 ea906c836569 615718ca496c7 84867056a693 88c25e6abb00 4499e580db9cDiscrete Mathematics Proving identity Problem A pair of i < j such that σi > σj is an inversion of a permutation. Let the number of permutations in Sn with k inversions be denoted by I(n, k), The task is to Prove the identity belowpassing through (9,5) with x-int ecept -3