9. Show that F= field? T a b a | a, b € Z5 is a subring of M2(Z5). Is Fa be Z5

Q: 6. Evaluate f z z* –8 dz. A) (x² - 8) +C B) a O b O d

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Q: Decomposition fields are algebraic extensions.

A: Definitions:Decomposition fields(splitting field) :  A splitting field of a polynomial p(X) over a…

Q: Which theorem can be used to prove that ARQM APMQ H R P M

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Q: I. Find A + B, where a) A = 1 0 41 b) A = 1-1 2 2 1 L 0-2-3 J -1 0561 L -4 -3 5-2 J [-13 3 5 1 2 2…

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Q: Recall the property that (a, b) = 1 if and only if ax + by = 1 for some integer x, y. Use this…

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Q: 6. Prove that x² dx b³ - a³ 3 3

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Q: 5. Prove that (Z, × Z6)/((2,3)) S Z12.

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Q: ALL for f*) Such tatt FIND FUNC TIONS Vx - x² +1 :(^),f

A: The given derivative of a function f(x) isf'(x)=x-x2+1x

Q: Determine whether (p→q)→(q→r) is equivalent to q→r. Justifyyour claim.

A: we have to check whether  (p→q)→(q→r) is equivalent to q→r

Q: is o(x). Hint: Use ling divisim

A: Let consider  fx=x4+x2+1x3+1 To show that f(x) is O(x).

Q: f6) = 5-31 5+3x Q11. Let %3D

A: Given: To Find:

Q: S S( 3x² +x³y)dxdy

A: Evaluate ∫13∫023x2+x3ydxdy=?

Q: AN 3. Given R(x) = a) R (-1 3x-1 TED COMPILED ANDEDIB COMPILED AND EDITE COMPILED AND SoCOMPILED AND…

A: This is a composition of functions.

Q: all your calculations and simplify your answer completely. Il you only give a final an- Swer you…

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Q: 9. Which of the following is one of the possible answers when you integrate the expression 2csc² x?…

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Q: |-2+1 () 7:2 だ,て メ-ドコ X, +1メ」 メレ-3x, transformation is gi ven t of trensformation; 4) Show that it…

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Q: Determine whether the function defined by = 2x1y₁ - x1y2 - x2y1 + 2x2y2 is an inner product on R².

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Q: verify that (A + B)C = AC + BC

A: To verify that (A+B) C = AC + BC.

Q: Use with (8'e) (-2,) (7,1)

A: Given query is to find indicated vector operation.

Q: P → (Q → R) is equivalent to A. (P ^ Q) → R B. (P v Q) → R  C. (P v Q) → ∼R D. None of these

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Q: = Suppose (3, −1, −2), = (-1, 1, −4) and w = . 9. 9. v.w= 9. v. v= ū⋅ (v+w)= . 9. (5, 1, 1). Then:

A: For any query with the solution, please ask in the comment box.

Q: dr J (9 – 4r2)3/2

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

Q: 19 a) Edur 1+2r 1 b) (1 +25), | E dr

A: We will solve  the integration.

Q: 2) Let T [ ] = DT [₁2 i] = i) 0 ii) 2T = 1 + (-c-d)x+ (-d)²x² + (a + c)³ x³. Then we have: -7 - =

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Q: 33. What is the real part of In (2 + j2)? a. 0.785 b. -0.785 c. 1.040 d. -1.040

A: 2+j2=2√2(1/√2 + j/√2) = 2√2(cos(π/4)+jsin(π/4))

Q: For two real numbers x and y, if 2x + 3y > 7. Prove by contradiction: 18, then either x ≥ 3 or y ≥…

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Q: Evaluate by Algebraic Substitution: * 5. S/1+vz dz -(1-v5)(3VE – 2) +c b. (1+ v7)(3V7 + 2) + C 5(1 +…

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Q: Disprove: X={r1, 12} iff V, (z E X +x=VI=T2)

A: To do: Disprove the statement…

Q: 471- 30. √2x-1=7 32. √6-2x = 4

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Q: — 2х1 — 5х2 + 8хз x1+3x2 – 5x3 +x4 |3x1 + 11х2 — 19хз + 7x4 X +7x2 — 13хз + 5х4 x1 X2 . Let T X3 X4…

A: The given transformation T can be written as            Tx1x2x3x4=-2-58013-51311-19717-135x1x2x3x4is…

Q: What meaning can be attached to this cross product: r the toolbar, press ALT+F10 (PC) or ALT+FN+F10…

A: The cross product of two vectors A→ and B→ is given by; |A→×B→|=|A→|×|B→|×sin θ And the cross…

Q: 5. /(들+ 4) dt + 4t3 ) dt is -+ t+ + C, b.는+ t® + C,c.는+t+ + C а.

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Q: 2.2.12 Prove that if x and y positive real numbers, then Vx+y # Vx+ Vy. Argue by contradiction. are

A: Let x and y are positive real numbers. Also let x+y=x+y Now squaring on both side,we get…