-1 -2 -3 -4- 1 3 Let A = 1 1 1) Compute det (A) using the cofactor expansion along the fi 2) Find adj (A). 3) Compute A-1 using adjoint.

Q: z -7 2. prove that: Im(z)= 2i

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Q: Define an by an for 4an-1 +5an-2, n 2, ao = 5, a1 = 13. Find an explicit formula %3D an

A: an=4an-1+5an-2 an-4an-1-5an-2=0 for the homogeneous system, write the auxiliary equation  r2-4r-5=0…

Q: Prove the identities. 9n Afn-fn A9. In gnti %3D gn

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Q: Let z = 10 e7* i/6 Write z, z6, z8 and z-2 in the form a + bi. 7n () z = 10e + 0i 26 -1000000 + i0…

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Q: -5 7 Eхample 61. Find the adjoint of A = -2 and show that A (adj. A)=|A| I.

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Q: 27 de Evaluate the intergal using the residue theorem. 15 +3 cos 0

A: residue theorem of integration

Q: 6. The set A = {0,1,2,3} under multiplication modulo 4 Kni 7. R = {eskmt : k e 0,1,2,3,4} where e10…

A: Group theory

Q: Let O 3i] A = %3D 3i 6] Find the Laurent expansion of the resolvent of A around the point z = 3.

A: Given: The given: A03i3i6 To find the Laurent expansion of the resolvent of A.

Q: -3 0 1 1 1 2 -4 1. Let A = -2 1 -6 3 -4 2 Compute det(A) using cofactor expansion. Indicate the row…

A: Given  A=112-3-40-10-21-6032-42

Q: The Fibonacci numbers 1, 1, 2, 3, 5, 8, 13.. are defined by the recursion formula xn+1 = Xn + xn-1,…

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Q: If {an} and {bn} are divergent, then {anbn} is divergent.

A: Given; (an) and (bn) are divergent.

Q: Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the…

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Q: apply Residue theorem to find the 2n cos20 dð. o 3+2sine

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Q: Evaluate det(A) by a cofactor expansion along a row or column of your choice. 3 3 5 2 0 -2 (a) A= 4…

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Q: (b) Determine the Z-transforms of the following expressions 6n+5(n+1)-4(-8)" (i)

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Q: -1 1 -3 Let A = 1 Use a co-factor expansion (expansion by 4 -2 minors or Laplace expansion) to…

A: we have to find det(A)

Q: 2. (i) (ii) Prove the following results : cov (x2, x1.23)=cov (x3, x1.23)=0, cov (E 1.23, X1-23) =…

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Q: We define the "column j expansion" by : det A = (-1)*+3 Aij det(A¡j) 2 0 1 2 -1 2 1 1 (a) Use the…

A: Given: Column j expansion for determinant of matrix A is given by, det A = ∑i=1n(-1)i+jAijdet(Aij~)…

Q: Let n >1. A hexagonal number h, is of the form h, = n(2n – 1). - a. Determine the first 5 hexagonal…

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Q: If {an} and {bn} are divergent then {an + bn} is divergent. a) true b) false

A: From the Convergence- divergence theorem. If an and bn converges then an+bn always converges.

Q: Exercise 195 Further problems on Leibniz's theorem 8. If y = (x³ + 2x²)e2* determine an expansion…

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Q: Let A = 2 4 -2 03 3 5 1 -1 (a) Find det(A) using the cofactor expansion along the third column.…

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Q: Let A= 3 (n) Compute det (A) using a cofactor expansion along row 2. (b) Find A adj(A). (c) Find det…

A: Result: If determinant of matrix is a than determinant of  inverse of matrix is 1a. Transpose of…

Q: Find the conjugate and modulus of the following: (i) (1 + i³) – (4 + 3i) + (7 – 9i*) (ii) 7 +i° + (6…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Evaluate det(A) by using expansion along a row or column, given

A: Given:         A = 01201345-20-111-100   To find :     det(A) using expansion along row or column

Q: 11. Let co denote the set of all infinite sequences x = (r1, 12, 13,...) of complex numbers such…

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Q: b) Show that P1(cos(0)) and P2(cos(0)) are orthogonal to each other, P, and P2 being Legendre…

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Q: -3 Given matrices A-B and B- and B= , verify that det (AB)= det(A). det(B). Find the third Taylor's…

A: (i)

Q: 1- Find the and argumint g fallowing modulus the Complea numbers 2+i 2+ i 3-i 4i + (Hi)?

A: It is given that

Q: Example 8-13. If X ~ B (n , p), show that : E(X-r)* = " ; Cov (, X) =- pq n

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Q: Prove that Pn(1) = 1 and Pn (-1) = (-1)"

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Q: Prove the Identity H8= A(++÷)(1+ 4) %3D 2.

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Q: (6.1) Find det(C) if A A+1 C = A- 1 (6.2) Use the cofactor expansion to determine 2 0 0 0 3 1 2 0 2…

A: Since you have posted multiple questions we solve first question for you To get the solution of…

Q: [1 0 2 0 2 A = 7 1 1 then the cofactor A21 of a21 is: Select one: O None of the other choices. O -2…

A: The given matrix is; 1 0 2 0 2 5 7 1 1.

Q: Find the Laurent expansion of g(z) = (2-1)/[23+322 +22] in i) 0 < 2 <1 ii) 3<|z| 0<z +2 <1 E

A: As per guidelines we experts are allowed to solve three sub-parts at a time. Please reupload the…

Q: The modulus of 5 + 4i is * O-41 O-√41 O√41 041 The conjugate of (i-i²)³ is O-2-21 2+2i -2+2i Oi-1

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Q: 22. Given that Z= 2-3i, express Z/Z* and Z(cos-- isin -) in the form a + bi, where a and b are real…

A: Note: "Since you have asked two questions, we will solve the first question for you. If you want any…

Q: (2C, + 6C3X + 12C,x2 + 20C3X + 30Cgx +.) + C,x + Cax + ...) = 0 Collecting like powers of x. (2C2 +…

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Q: 2.2.6. In the text, the modulus is defined in terms of the inner product. Prove that this can be…

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Q: { (3i – 2)² = -n(6n² – 3n (b) Prove by induction that | i=1

A: We have to prove that ∑i=1n3i−22=12n6n2−3n−1 for n≥1 by using principal of mathematic induction.…

Q: polynomial in V2+i and compute the conjugates of i over Express i as a Q(/2 + i).

A: As per the question we have to express i as a polynomial in (√2 + i) and then compute its conjugate…

Q: 5 +1 Tsimplify denomina 7) (1+i) (1-1) = 4 the Following without using the de noctor Prove that

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Q: 2 3 Let A = -1 2 3 -2 1 (a) Find adj A. (b) Compute det(A). (c) Verify Theorem 3.12; that is, show…

A: A=213-1203-21 We need to find adj.A det(A) Verify Aadj. A=adj. AA=detAI3

Q: 8 6. Let A=|3 5 7 | 4 9 (i) Evaluate det(A) by cofactor expansion. 2 (ii) If A is invertible, find…

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Q: Let A= 3 1 3 (a) Compute det (A) using a cofactor expansion along row 2. (b) Find A adj(A). (c) Find…

A: A=1-12031-131 Cofactor corresponding to 0 is given by -1231=-7 Cofactor corresponding to 3 is…

Q: Let а — 3 1 A = 7 -1 8- a 2 6 а — 1 (a) Find det(A) by cofactor expansion with respect to the second…

A: The solution is given below in the next step:

Q: (2.5) Find another representation in which a. r is negative and °<0 < 2n. b. ris positive and -2n <0…

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Q: (a)] Show that 1+(1+z)/2 csch z In • [(b)] Use part (a) to find all the values of csch (-2i).

A: Let:

Q: 2. Let zl = 3 + 4i, z2 = 2-i. Answer the following quextions: a. The conjugate of z1 is b. The…

A: Given z1=3+4i and z2=2-i We need to find a) conjugate of z1 b) modulus of z1 c) z1+z2 d) z1-z2 e)…