1 2 Find a mat rixP such that P 0-1 0 -1 1 0 OA. 1 1 1 -1 | P : O B. 1 1 0 - P. OC. %3D 1 1 1 0 %3D OD. -1 1 P= OE. 0 1 P.

Q: Find a mat rixP such that P-1 I 0 2 1 0 0 2 1 0 P = OA. 1 0 P = O B. 1 1 -1 0 P = OC. 1 1 OD. 1-1 P…

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Q: 1. 1) Lt c the below figure- be the closed contorer quen in is d Z =-2 i ? so

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Q: 4. [MO51] Classify the following PDE: a. 2 uxx = Uxy – 4uy a²u au du b. ax2 + 4 +3 +u = 0 + дхду ay?…

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Q: 6) Suppose V is a finite-dimensional with dim V > 1 and T e L(V). Prove that {p(T)lp € F[x]} # L(V).…

A: The complete solutions are given below

Q: 2 20 Let A = Which of the following is a consequence of the Cayley -Hamilton Theorem? 2 10 L-10 0]…

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Q: Find the value(s) of k such that A is singular.

A: The given matrix will be singular if the determinant of it is 0

Q: 1 0 Find a mat rix P such that P- 23 1 0 0 3 1 1 %3D OA. OB. P В. -1 0 P = O C. P D OD. 1 0 P =D OE.…

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Q: 1. (a) Consider the set S = {n(-1)" : n e N}. Verify the existence or otherwise of Min(S) and…

A: a) The given set is,S=n-1n:n∈ℕ

Q: 3. Find two elements a and b in Z25 such that a and b are units, but a +b is not a unit. Justify…

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Q: ands 1. Let m*(A) = 0. Prove that for every B, m" (BUA) = m" (B). %3D %3D

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

Q: Prove this! P (an) = W/ NM) [M-N (p-q)" ] 8 Npq %3D exp

A: your question is not clear i think some error in the question plz confirm it.....

Q: 1 0 Find a mat rixP such that P 0 2 1 0 P : %3D 1 0 OB. 1 0 P = -1 1, P = OD. 0 1 1-1 P 3D OE

A: In the question we have to find matrix P.

Q: 30 Find a mat rix P such that P- 1 0 O A.P %3D 1 0 O B. P= 1 0 Oc.P = 1 O D.P = 1 1 O E.P=

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Q: (a) Let a > 0. Using the substitution t = In x or otherwise, prove that In a e 4/a² - e 2t dt =a5…

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Q: 2 Q) Let A € M₁ C4) such that A² = A ENA show that det (I+A) = 2

A: If minimal polynomial is totally factorizable that is product of linear factors. Then matrix is…

Q: Find a mat rix P such that P 1 0 1 0 P= 23 0 3 1 1 -1 А. 0 1 1 0 P = O B. 1 P = OC. %3D 0 1 1 0 P =…

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Q: 2.2.15. Let X be a metric space, and suppose that xn → I and yn → K. Prove that d(xn, Yn) – + y in…

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Q: No By Cantor's theorem No=2"°. ylgn ihi

A: Since aleph not is transfinite no.  And we know 2^alephnot=continum.

Q: Prove that P(Ø) = 0. Hint: Let A, = Ø for all i in equation (1.3.3).

A: Consider that

Q: 20.* a. Let P(z) = 1 + 2z + 3z² +.. of P(2) are inside the unit disc. + nz"-1, By considering (1 –…

A: Proved by using Rouches theorem from complex analysis.

Q: Assume that |Xn] 0. (Hint: first, prove that P(|X|>c+1) = 0.)

A: Answer:

Q: 4. [MO51] Classify the following PDE: a. 2 uxx = Uxy- 4uy a u b. ax2 a u a2 u ne +3 +u 0 +4 ne +. ay…

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Q: 1 0 Find a mat rix P such that P-' 1 0 0 3 23 1 -1 0 1 O A.P 1 1 O B.P В. 0 1 1 0 C. -1 1 1 0 OD.P…

A: Let P = abcd , where ad - bc ≠0 Now , given  P-11023P = 1003 Now pre-multipyling by P nad…

Q: Find the value(s) of k such that A is singular.

A: A matrix is singular if its determinant value is zero. So we find the determinant value of the given…

Q: 2. Find +he source (メ) Q (x) that the So lutiom U (x it) of k + Qx) 2 - 0 l• Con e

A: given equation ∂u∂t=k∂2u∂x2+Qx,       -∞<x<∞           ...iux,0=0 claim- to find the source Qx…

Q: (2) Show that if dim(V) = k (so in particular, T has k distinct cigenvalues), then there exists v e…

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Q: 6 7 /hat is [AB, the coordinates of A with respect to the standard [2 4 [o _0 1 1 asis B = of R2x2?…

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Q: 2 1 Find a mat rix P such that P- 0 3 1 0 P = O A. - P = ОВ. 1 %3D OC. 1 -1 0 P = O D. 1 1 11 P = O…

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Q: Find a mat rix P such that 30 P%= 1 2 30 0 2 1 0 OAP = %3D 3 -1] 1 0 OB P -3 1 -1 0 OcP = %3D 1 0…

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Q: MAC 2313: 15.2 Worksheet 1. Evaluate ffr cos ydA, R is bounded by y = 0, y = a?, a = 1.

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Q: Find a mat rixP such that P 1 2 1 0 0-1 0-1 -1 0 OA 1 1 1 0 P = 1 1 OB. 1 0 OC. -1 1 1 -1 P = OD. 1…

A: here option  (a) is true because

Q: Let n E N coprime with p. Show that there exists x, y E Z coprime and such that p | x² + ny² is and…

A: To prove the given claim we have to show that :- x,y ∈ Z ; gcd(x,y)=1 ; p | x2 + ny2   implies…

Q: 1/2 Show that ||r|| = + [En]² defines %3D a пorm. j=1

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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: 1 Find a mat rixP such that P 1 -1 1 0 0 2 0 2 1 1 P = O A. 0 1 -1 0 OB. 1 1 P = OC. 1 0 1 1 1 P =…

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Q: Express the following tunctrons in the form u+iv f(2)=In (I+z)

A: Solve the given problem.

Q: EX: Find the Z. T. of X(X) = cas wok u(k) Soin

A: Z transform of the function

Q: enoitetimil torte stigasb = 4", where m, neN. 10. Prove the identity: 3 r=0 itong s

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Q: 13 1 0 Find a mat rix P such that 0 2 0 2

A: Find matrix P such that P-11302P=1002

Q: 1. Prove that L(t)=. 1 s2

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Q: 1. Prove that L(t)=. s2

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Q: Find the value(s) of k such that A is singular.

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Q: 1 Find a mat rix P such that P-1 1 0 0 2 0 2 1 0 O A. -10 P = OB. 1 1 P = C. 0 1 P = OD. P = O E. 1…

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Q: 9. Let S- {xeZ| 3r.seZ,x=9r+6s) and T={xeZ| 3x} b) Prove that T Cs. a) Prove that SCT. Hint for (b):…

A: Part(a) We have S=x∈Z/ ∃r,s∈ℤ, x=9r+6s and T=x∈ℤ 3/x  Now, let a=9r+6s be an element in S. Then…

Q: 1 0 0 1 0 111 Let A = then detA using the big %3D 210 1 10 0 1 formula is

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Q: ZH E LI and HI 1 GJ. Complete the proof that AGIJ S AGHJ.

A: Here we use two concepts  1) sides opposite to equal angles of a.         triangle are equal. 2)…

Q: Find a mat rixP such that P [1 2 1 0 | 1 0 P = O A. -1 1 1 - ОВ. 1 P= OC. 0 1 -1 0 P = O D. 1 1 1 0…

A: Just multiply both sides by P from left side and set P as 2×2 matrix.

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: -- a) such that ab =1. Let p>1 be a prime number. Show that for each a + 0 in Zn there is b in Zp…

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Q: QR I RS and UV 1 TÚ. Construct a proof that ZQRS = ZTUV.

A: First, we sketch the situation roughly  We have to prove:

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.