Let a = (1432)(257)(654). (a) Find a disjoint cycle decomposition of a, i.e. write a as a product of disjoint cycles. (b) Find a transposition decomposition of a, i.e. write a as a product of transpositions. (c) What is the order of a? (d) Is a an even or odd permutation?

Q: Find the multiplicative inverse of 3 in GF(13) domain using Fermat’s Little theorem.

A: We have to find the multiplicative inverse of 3 in GF(13) domain using Fermat's Little Theorem.…

Q: | 0 0 1 1 1 00011 0 0 0 0 1 5 (If the arithmetic for computing an entry involves huge powers, you…

A: As per bartleby guidelines we are allowed to do maximum of 3 subparts

Q: Find the QR decomposition and prove -3 -5.

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Q: A polynomial expression is given. 3z (zy) 21'y Which is an equivalent form of the expression? 3y 3y

A: Explanation of the answer is as follows

Q: Give a combinatorial proof of the identity (2)=3(") + ³(²) 3(3).

A: The combination formula is defined as (nr)=n!r!(n−r)! Therefore…

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Q: 19 (e) a = 1575, b = -231 (a) 3710

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Q: Divide the polynomials by using an appropriate method. (8x" – 16k10 + 24k° – 32k*) + (84®) = O olo

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Q: how do you write (14)(27)(523)(34)(1472) as a product of disjoint cycles

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Q: Example 1: What is the product of-4x and (x+2x-4)? Box Method "FOIL" Method Try It Problem #1: Find…

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Q: What is the rule for this pattern? (figure 1 is 1 block) Of(x)=n+2 Of(x) = 2n Of(x)=n-1 Of(x) = 2n-1

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Q: (2) (a) What is the order of (Z20, +20)? (b) What is the order of (Z20, 20)? (c) What is the order…

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Q: Example 2 Compute (a) (1+i)/(3-i) and (b) (1+i)4.

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Q: Using the recursive relation I (r + 1) = r[ (r) and the fact that I ย relat 1 2 }} 5 {} and (b) £ =…

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Q: -2 Use Gauss-Jordan Method to find the inverse of -4 1. 1

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Q: Determine the simplified form of (4 – 37) (–9 + j) – (8 – j5).

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Q: Let z E (-1,0) and let R, (z) be the remainder in Maclaurin's formula for In(1+z) in Cauchy's form.…

A: Given the function is fx=ln1+x

Q: What is the order of Z11?

A: Recall the fact that order is the number of elements in that group. Note that ,…

Q: (n² + 6n – 4)(2n – 4)

A: The polynomial is given by n2+6n-4(2n-4)

Q: Find the general solution of the recursive relation an ○ an = a (1 + √√14)” + ß(1 − √√14)” an = a(1…

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Q: In the characteristic polynomial (3 – A)(4 – A)³(–3- )(3 – 1), what is the multiplicity of d = -3?

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Q: (c) How many of the elements of Z186 have multiplicative inverses?

A: To find the number of elements in the set of integers modulo 186, which have multiplicative inverse.

Q: H.W Compute the following products: 7 a. 1/3] -2 31 7 -6 21 ь. [3 -1 4] х| 5 1 -4

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Q: 5. Evaluate a. 3! ×4! 5!

A: According to bartleby guidelines we only provide one solution at a time. Solution 5.  3!×4!/5! We no…

Q: (a) Explicitly check that [7] + [21] = [98] + [–5] in Z13- (b) Find another value of n such that [7]…

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Q: If GCD of (a,b) is 1 we can find the lcm by multiplying a and b. True or false

A: if GCD(a,b) is 1, We can find lcm by multiplying a and b.   This statement is True.

Q: Show thet tegular a S(G) = A(G). G

A: Let us assume that graph G is regular. Now,  δ(G)= degree of the vertex with minimum degree…

Q: Find the characteristic polynomial of A

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Q: Find the characteristic polynomial of 10 - 1 5 4 - 4 0 6

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Q: Which property of polynomial multiplication says that the product of two polynomials is always a…

A: To answer which property says the product of two polynomial is a polynomial.

Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus. 

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.