3. Prove that A=I-N+N²_N³ for A & N defined as follows: N=A–I (identity), where 1 0 0 & I=|0 1 0 1 a12 d13 A=0 1 A 23 1 0 0 1

Q: Find the value of k such that A is singular. 1 0 5 3 -1 0 2 k k =

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Q: Which of the following is correct? 1 A. X(z) of B. X(z) of -n7"u(-n-1)= C. X(z) of -n7"u(-n − 1) =…

A: Note: Hi! Thank you for your question. As there are multiple questions so as per our guideline we…

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A: Using complex properties.

Q: Find the value of k such that A is singular. 1 0 4 5 -1 0 3 3 k k =

A: Topic:- Matrix

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A: Solution:     Let 3 does not divide n      =&gt; n = 3k ± 1 for some integer k.       =&gt; 2n2 + 1…

Q: 3. Show that if A-1 exists, then f eAT dr = A-(eAt – I) = (e4t – I)A-1.

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Q: 1 and that p= V3 1 + k 1- k' Given that k = express in its simplest surd form (i) P, 1 (ii) P :-

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Q: (b) Let A¡ = [-i, 1] for every positive integer i. Find U A¡ and N1 Aj.

A: Given that Ai=-i,1 for every positive integer i. That is, A1=-1,1, A2=-2,1, A3=-3,1 and so on. To…

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Q: Find the value of k such that A is singular. 1 0 3 4 -1 0 2 4 k k =

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A: From the given information,  (Wt, t≥0) be standard Brownian Motion. Note: In the given situation,…

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A: From the given information, U1, U2,.... are iid and each uniform on [0, 1]. fUi=11-0, 0&lt;Ui&lt;1…

Q: 2. Determine the following sets: a) {r €R: (3n EN\{0}) 2n – 1 < nx < 7n - 2} b) {r ER: (Vn EN\{0})…

A: An interval is nothing but a subset of the set of real numbers. When the two endpoints are included…

Q: If (n + 1)(n + 2)an+1x" - nan-1x" = 0, n=1 show that for k = 1, 2, 3, ..., we have 1.3.5... (2k - 1)…

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Q: 7. (Hadamard) For any real nxn matria m 1/2 A)] < ΠΙΣa; and |det(A)| Σ i=1=j=1 holds iff either A…

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Q: 3. For all æ E Z[i], there are N (x) elements in Z[i]z.

A: The set of Gaussian integers is a subset of the set of complex numbers containing the elements with…

Q: -1" n! 1. Prove that S xm (In x)mdx (m+1)n+1

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Q: 10. Let X , j= 1,.., n, be i.i.d. r.v.'s such that E(X,)= µ, o'(X)=o', both finite. j' Show that E(X…

A: The normal distribution: A continuous random variable X is said to follow normal distribution if the…

Q: 28. Prove by induction that i(i – 1) (n+1)n(n– 1) i=1 holds Vn E N,n 2 1.

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Q: 1.Prove o* In°(x) d.x 1+ x2 8. 1 1 3n +2 n=0 Σ 1 3/3 Зп + 4 ||

A: Given : ∫0∞ln2x1+ x2dx = π38 To prove the above integral

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Q: 1. Condense and expand. a) Condense as a single quantity: 1 In(3)+- In(x? +1)-3 In(1+x) 3 b) Expand:…

A: Given, (a)  To condense ln3 + 13ln(x2+1) -3ln(1+x) (b) To expand lnx2+1x+2(1+x)5

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Q: Select all of the following that are equivalent to >(2) +> (3k + 1)? k=0 k=0 п+1 A. O) (3k + 3) k=0…

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Q: o.10. Prove that (a) J,"(x) = ¿[J,(x) – 2J,(x) + J, + glw). n n-2 n' n+2

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Q: 3. Let A = {3k : k € Z} and B = {15m + 12n : m, n € Z}. Prove that A = B.

A: Let     A = {3k : k∈ℤ}    and          B = {15m+12n: m,n∈ℤ}To show :- A=B∵Let  x∈B  ⇒x = 15m1+12n1…

Q: show that if Z ~ N(0, 1) and Y ~x²(n) with Z and Y to be independent, then T: n

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Q: Let z = x + yi, z, = 1- 0.5i, and z, + z, = 3-1.5i. Find In(z,) - In(z2) C) In(50) + 2nin A) In(25)…

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Q: 5. Let h (z) = (z+1)(z+6)(z+10) z(z+2)(z+3) (z+3)(z–2)°, (z+2)(z+6) What is the residue of h (z)at z…

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Q: If t,= 4n+1, find t,, t,, t3, and t Express t n+1, in its simplest form. n+1 In-1

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Q: 4.3 (i) Let X ~ N (µ, o), and for 0 x1-a) = a, so that P(x, <X< x1-a) = 2a. Show that x, = u +o$²…

A: here X is normal distribution. 0&lt;alpha&lt;1

Q: 4. Prove that d x" = nx"-1 ミクー! de

A: To prove that ddx(xn) = nxn - 1

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Q: 8/14 Let 1 < p < 0. For t = [0, 1], let xi(t) = 1, -{ 1, if 0 ≤t≤ 1/2 -1, if 1/2 <t≤1 and for n =…

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A: Solution: Let us consider the symmetric group Sn, for some positive intiger n.  We know that Sn is…

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: that N(ry) = N(x)N(y) for all x and y in 22). 2. If x is invertible in Z[1], show that N(x) must…

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Q: Find the value of k such that A is singular. 1 0 6 4 -1 0 6 2 k

A: Given. A is a 3X3 matrix. We need to find the value of k for which the matrix is singular. Singular…

Q: Find the value of k such that A is singular. 0 4 6 -1 0 4 2 k k =

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Q: (28) Suppose 1 <N < w and h : w → N. Show that there exist a < b < c < d <e<w such that h(a) = h(b)…

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Q: Let 0 3 0 6 3 A = B = 1 0 1 O 2 0] 3 -2 -4 C = 3 -2 -4 3 6. 3 7 (a) Compute AB. AB = (b) Compute AC.…

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Q: 12. Prove the following (A+ BB")-B= AB(I+ BT AB)-1 by express the B+BB' AB in two forms. O Type here…

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