(b) Prove or disprove that det (ABCD= det(A)det is jaett Jaet(D)

Q: Prove Theorem (A + B )T = AT + B T

A: Prove Theorem (A + B )T = AT + B T

Q: 3.) Prove (cA)" = cCA) %3D

A: Let A be a m×n matrix so A=(aij)  1≤i≤m and 1≤j≤n ie A has m rows and n columns. By AT we mean…

Q: Discuss the Singulazities and Poles of fiz) = zéSinz (z-2) (zこいこょうと+ら)(2t (こか) +4

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Q: If la,} and {b„} are divergent then {a, + b,} is divergent. True False

A: Given: an and bn are divergent . The objective is to state whether an+bn is divergent is true or…

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A:

Q: If u xv=uxw and u ‡ ♂, then u = w.

A: The given statement is: If u×v=u×w and u≠0→, then u=w

Q: det(A) Show that det(AB-') = %3D det(B)

A: Consider, Let A and B be the two n×n matrix, Now Consider, detAB-1 We know that the theorem, Let A…

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Q: 1 dæ using the residue theorem. (2² + 1)° Evaluate the improper intergal -00

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Q: 5. What is UF, where F = Ø? Prove the correctness of your %3D | computation. answer

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Q: d csc 'x dx -1 Prove that xVx? – 1 2.

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Q: 2- Let z=x+iy. Find a) Img(1/2) b) Re z c) Img (1/z')

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Q: dik koordinatylarda x,y öyleki x kare artı y kare küçüktür beş denkleminin grafiğini çiziniz

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Q: a) Show that fi (x) = x, f2(x) = cos 2x are orthogonal on

A:

Q: 2. Let X, Y c R. Prove that X U (Y – X) = Y if it is true. If not, give counterexamples to explain.

A: Given statement is false.

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Q: An electromagnetic wave does require a medium to travel. O True O False

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Q: 9. Prove (1, sin z, cos z} is linearly independent in [0, 2x].

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Q: b) g(x) = S,* In(2r + 1)dr

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Q: 5. What is UF, where F = 0? Prove the correctness of your %3D answer / computation.

A: To find- What is ∪F, where F = ∅? Prove the correctness of your answer/computation.

Q: Prove that TIN) F(a – p) O< Re

A:

Q: Prove that Ix I - I y I ≤ I x - y I.

A: We have to prove that  x-y≤x-y We know, x+y≤x+y Then,  x=x-y+y⇒x=x-y+y≤x-y+y⇒x-y≤x-y

Q: Verify Young's Theorem z = In(2x + y) -

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Q: 3. Prove the pythagorean Theorem

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Q: 6) limSin (0 – ) 3. 2

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Q: Prove Theorem (AT )T = A

A: Given: Theorem, ATT=A.

Q: 3) Given: BAC= AHC=90°. %3D Prove that: B= HAC and C= HAB. %3D %3D H. C

A: We will prove the given problem.

Q: Use Cramer's rule to solve for y without solving for the un- knowns x, z, and w. 4x + y + z+ w= 6 3x…

A:

Q: Compute the discriminant D(x, y) of ƒ(x, y) = x2y2.

A: fx, y=x2y2 Partially differentiating with respect to x, we get ∂f∂x=2xy2 Partially differentiating…

Q: What is Rolles Theorem and how do you find "c"?

A: What is Rolle’s Theorem and how do you find c

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Q: (4+38)-(9 -J2) Rectangular ?

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Q: (a) Let r = ri+ yj + zk and let r = ||r||. Prove that - (1) a

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Q: dual of c, is isometric to l'.

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Q: - seyi + avīj + () dt = 3 3

A: We have to perform integration by parts and then insert given limit

Q: Q(x) = √3/2+² Ser fet de Prove that & QQ (-∞ ) = 1

A: Here we can use Gamma function formula Γn = ∫0∞ xn-1 e-x dx to evaluate the given improper integral.…

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Q: 21. xª sen z dz -z' cos z + 3z² sen z + 6z cos z 6 sen z + C %3D

A: see below the answer

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A: Here,we have to prove that Res(tanz,pi/2)=-1

Q: 3 and ajj = i. j. Th

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Q: on vectors for t2 0.

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Q: Which part (Given or Prove) of the proof depends upon the a) hypothesis of theorem? b) conclusion of…

A: (a) Hypothesis of the theorem :             The hypothesis of the theorem is been used for the…

Q: Ex Using Cramer's Rule to solve the sys x-y+z 0 2x +y-3z = (x+y+z%3D

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Q: mith Exe:- Jk +3 - tyk+Z +ZYkxi +36Yx =1+2

A: