Suppose a and ß are transpositions, then show that if aß= (1), then a = B.

Q: In the expansion of (x+y)35

A: We use the Binomial Theorem to find the required coefficient in the given question.

Q: Show that if AB = AC and A is nonsingular, thenB = C.

A: Given that  A is invertible matrix. It means inverse of A matrix is possible. A is non-singular…

Q: Ques uon 8) Choose |/| from the following: a. 05829 b. 0.6062 c. 0.6305 d. 0.6557 e. 0.6819 1.…

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Q: If (0,1) ~ (-1,1) and (-1,1) ~ R. Deduce that (0,1) ~R

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Q: Let a=⟨3,−5,5⟩ and b=⟨−1,5,2⟩ Find the component of b onto a

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Q: for which the giyen system has no

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Q: * If Iz| = Re(z), then z is

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Q: Show that under the transformation: k= the equally spaced z-values, z : 1o, To +h, xo +2h, .…

A: Just substitute the given values of x and proof will follow.

Q: (i),if i = j + 1)',if i = B = A-, if i +j mif i + j

A: Here we have to find the Matrix A and B then find the product according to the question, now the…

Q: How many elements are in Z5[i]/<1 + i>?

A: Given Data The expression is Z5[i]/<1+i>.   Consider the Z5[i]/<1+i> in the form of…

Q: If z, = 3+2). z, = 4 - 8j and z, = 2+5j , find the conjugate of: (a) z, + 22 (b) z, -z, (c) z, (d)

A: Given, z1=3+2j, z2=4-8j & z3=2+5j To find conjugate of, (a) z1+z2(b) z1-z2(c) z1z2(d) z3z2

Q: Compute A - 31z and (313 )A, where A =

A: Given,       A=5-14-44-6-321

Q: The order of the element 3 in Z24 is

A: Given: Z24 Formula Used: The order of an element k in Zn is given by Ok=nhcfk,n

Q: Suppose that |u xv = 7. Find ||(5u + 6v) × (3u - 9v)||-

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Q: Compute Re if z₁ = 5√√2 + 2√3i, and z2 = 3√√√2-5√3i 2

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Q: If Ea, is divergent and Eb, is divergent, then E(a, +bn) is divergent. Select one: O True O False

A: Sum of two divergent series not necessarily divergent.

Q: =3. Let a = [2₁1,-1], 5o = [4₁-5, 3] and C-[-1,-2,5]. compute ax (b + c). Show full steps.

A: We have to solve given Questions.

Q: ) Show that Sn is generated by ((1,2),(1,2, 3, n)}. [Hint: Show that as r varies, (1.2,3. ny(1,2)…

A: Please check step 2 for solution

Q: Suppose an = 4an – 1 + 6an – 2 a4 = 96, a5 = 430, and a6 = 2276. Find а1, а2, and аҙ. аз. a1 Preview…

A: Here, recurrence formula is, an=4an-1+6an-2-2an-3

Q: If z- 6xy + y, find z, and Zy

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Q: Suppose z = a+ bi, w = u + iv, and

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Q: -AC || CD . AE || CB C. none of these D. AD || CB set Selection Co search

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Q: Given Ā =, B =,č = (a) Compute Ā· (B + T) (b) Compute A · (B × C)

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Q: verify that (AT )T = A

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Q: (b) Use part (a) to show that f (T) is either a transposition disjoint transpositions. or a product…

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Q: Shaa thut the graf of lincs iju fins rom F from E Iwhore is a iomasphic wilh Ge(5)

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Q: Suppose an = 5an-1+4an-2 – 3an-3 and a4 = 22, аs — 127, and ag = 717. Find a1, a2, and аз. ai = a2 =…

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Q: find A1 ∩B1 , GIVEN THAT                                             U= {x ∈ z/ - 7}    A= {x ∈ Z+…

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Q: If A is diagonalizable, then A is similar to D. Select one: O True O False

A: Given   if matrix a is diagonalizable then A is SIMILAR  to D

Q: Show that for n, m e Z+, gcd(2" – 1,2m – 1) = 2gcd(n,m) – 1.

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Q: If a is transcedental over Q then a^2 is also transcedental over Q

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Q: Consider a LU factorization of -2 1 3 A = 1 4 -2 -5 as A=LU. Then L2,1 and U1,1 are respectively…

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Q: Prove that if a, b E Z - {0}, then gcd(a, b) = gcd(a, -b)

A: soln:gcda,b=Greatest common divisor of a and bEvery integer that divides a and bsimultaneously will…

Q: If Ea, is divergent and 2b, is divergent, then E(a, + ba) is divergent.

A: Taking an example and than we are trying to understand tha statement.

Q: 6. Find Ar for A = and z= Az =

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Q: Suppose that  X  and  Y  are unknowns with  E ( X ) = 12 and E ( Y ) = 20.  If E ( X Y ) = 225,…

A: It is given that, E(X) = 12, E(Y) = 20 and E(X,Y) = 225.

Q: Consider the expressions: f1 = (Ax.((Ay. (y x)) y) u) 12 = (Axx y) a. List the bound variable…

A: Given: Variables applied in a function that are neither local variables nor parameters of that…

Q: Let Г3 -5 -1 A 2 3 3 2 В -3 -3 If possible, compute the following. If an answer does not exist,…

A:

Q: Let a-2-3j.kb-41-) and c-1-31-2k. If d is such that da-9. db-7 and dc-6, then d is equal to 01-31-2…

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Q: 2+13 Evaluate zdz along the following paths- (a) horizontally from 1 +i2 to 2+ i2 then vertically to…

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Q: Show that  1/3 Tn + 2/3Mn ) = S2n.

A: By definition, Tn=12∆xfx0+2fx1+....+2fxn-1+fxnMn=∆xfx1+fx2+.....+fxn-1+fxn…

Q: Create w = (1,3,5,..., 29). Give your R-code to subsequently remove all the components greater than…

A: R-code for the above problem is given as below: w= seq(from= 1, to= 29, by = 2)ww_remove <-…

Q: es of the matr

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Q: Show that S, is generated by ((1,2), (1, 2, 3, n)}. [Hint: Show that as r varies. (1.2,3. ,ny(1,2)…

A: Consider the group 1,2,1,2,…,n. That is group generated by 1,2 and 1,2,…,n. Claim: i,i+1∈1,2,1,2,…,n…

Q: . Let, a, = 1, az = 2, b; = 0, b2 = 1, for n2 3, a, = 2an-1 + bn-1 for n22 b, = br-1+ an-1 express…

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Q: Show that if E,=1 a, diverges, then En=1 | |a,| diverges. %3D

A: Given, We want to prove that

Q: 5 - compute – 5A 3 Given A 3

A: we have to calculate -5A

Q: In a AARG. if ZA = 72° and ZB = 63°, find ZC. 45 %3D

A: In a triangle the sum of angles of triangle is 180° Therefore  ∠A+∠B+∠C=180° substitute the value of…

Q: Suppose that det A = 3 and det B = – 1. Find det(AB³A™B-1)

A: Determinant Properties: 1) det(AB)=det(A) det(B) 2) det(A)=Det(AT ) 3) det(An)=(det(A))n 4)…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.