2. Prove that if a, b e R, then (a) -(a + b) = (-a) +(-b), (c) 1/(-a) = –(1/a), (b) (-a)·(-b) = a · b, (d) -(a/b) = (-a)/b if b # 0.

Q: (m) For ro = -8, 11 = -7, 12 = -6, 13 = -5, I4 = -4, f(z1)Ar,

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Q: 7 --y2 Then 2 5 Q2: If z = –x² az + 5x ду az 7y ||

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A: Using two sectant theorem,  ∠n=12x-y  Multiply both sides by 2. ⇒2n=x-y .....(1) Using intersecting…

Q: 28x+4y+kz -10 -5x-8y-4z = -2 e must have, k +|

A: The given system of equation is: - 6x + 4y + 7z = 3 28x + 4y  + kz = -10 - 5x - 8y - 4z = -2

Q: Show that 1 1 1 x2 y? z2 (y² – a²)(z² – a²)(z²? – y²) - - ,4

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Q: which of the folowiny -xト! is -3x 2 へ pove seies fore =e.e e E (-)"(-3x) n ハン 0 37 B. e (3x)" nこO *ス…

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Q: Verify that 2. 1 Hint: Consider x 0, x 0 separately

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Q: xy If z show that: x- y

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Q: 5. Show that b, is always positive, by establishing the equation (Qn-1,Qn-1) (Qn-2,Qn-2) b,

A: We will apply the properties of inner-product to prove the given statement.

Q: Give a counterexample to show that (A + B)-1 ≠ A-1 + B-1 in general.

A: Let  A and B be non singular matrix Determinant of A = 1 -0 =  1 Determinant of B = 1 -0  = 1…

Q: 1 Evaluate [ (x² + --- e2x +c 2 a) + In x+ b) 3 +C 3 e2x .3 c) + In x- d) + In x - 3 +c +c 2 2

A: We know  (1) integration of Xn dx =  Xn+1 / (n+1)  + C  (2) integration of emx dx = emx / m + C  (3)…

Q: Give a counterexample to show that (AB)-1 =/ A-1B-1 in general.

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Q: Express y as a fiunetion af k if y - 2r+5, 1- V3t -1, and t- 3k - 5.

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Q: How can I calculate using Excel?   Suppose X~N(193,7), and Z~N(0,1). Then x = 204, is equivalent…

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Q: Show that 1/3  Tn +  2/3 Mn  = S 2n

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Q: Let X,X2, ,X, be a ranc *(X), = 0*(1– 0)1-x; %3D

A: from above distribution is binomial  f(x)θ=θx(1-θ)1-x  ;0<x<1 E(x)= nθvar(x)=nθ(1-θ)…

Q: find x, y from [2 x + y 2 x - ] 3 3 3 O x=-9/2, y=-3/2 O x=3/5, y=2/3 none Q x=9/2,y=-3/2

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 2/3 Lal(2x²4). (2x+3 3

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Q: 12 y' (12x +5) (4y* +3)° b. If y* +3y-4x' = 5x+1, then prove that y"(4y +3) = 24.x--

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Q: Let æ² + y² + z² = 3xyz, th = 3ryz, th

A: Given that, x2 + y2 + z2 = 3xyz We have to find (del z)/(del x).

Q: (2) If U = (1 – 2xy + y²)-³ prove that, x- = y?U® %3D

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

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Q: Prove that the equation * + + = 1 has no solutions in positive integers x , Y, Z.

A: x/y + y/z + z/x = 1 if x , y , z are positive integers then case 1 :  If all three numbers are…

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Q: Prove that ∇2y8 = y8 − 2y7 + y6.

A: We have ∇yn=yn-yn-1    where ∇ is backward difference operator.

Q: 3 4 Evaluate [, S* 2dydx

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Q: 25. If ā = -j and b = 2x +5y, express and y in terms of ā and b.

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Q: 1. Find XY when X(-7, 10) and Y(3, 4).

A: GivenX≡-7, 10Y≡3, 4To find XY

Q: 8-JIE FCx²_ ye, y-z²) =• then Prove that + Xそ 2Z

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Q: Compute Projsw given by |2 -1 – 2 and S is defined by 8 [2 – 12]+t[-1 – 13], s,t e R. x = s ||

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Q: Use Cramer's rule to solve for z. Зх — 4у + z %3D 3 2х + 3у = 8 5y + 8z = 11

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Q: Show that |Aut(Z2 × Z2)| = 6

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Q: Express (i)(T) J3(x) in terms of J₁(x) and Jo(x) (ii) J₂(x) in terms of J₁(x) and Jo(x) (iii) J4…

A: Note: since you have posted multiple questions. As per our guidelines we are supposed to solve only…

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A: Since |z|=1 Let z=r(cos∅+isin∅) ⇒|r(cos∅+isin∅)|=1 ⇒r=1 Now

Q: S (sec5x – tan5x)sec5xdx - Select one: O a. (tan5x - sec5x) + C O b. (tan5x – sec5x) + C O c.…

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Q: 2. Evaluate f'(5) for y = v2x² – 1 hor Ju OIT

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Q: 19. (x, 4x), (-2x, 3x), given that x < 0 -XV10 (since x< 0, Vx2 = -x) %3D 20. (x, 4x), (-2x. 3x),…

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Q: Assume that y = 69 when x = -3, y=-72 when x = 15 and y = 99 when x = 27. If we…

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Q: Prove that y = e-3* (Acos 5x - Bsin 5x) + Cx; A, B and C are arbitrary constants will equalto y"(17x…

A: Given,            y =e-3xAcos 5x -Bsin 5x + Cx

Q: +prove by indirect method that i X+y >5 then or y>3. x>2

A: We need to prove that if x+y&gt;5 then x&gt;2 or y&gt;3

Q: 2. 1. If UZ = x+ 21 and ZS = 3x – 15, find US.

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Q: What is the zero-product principle?

A: Zero product principle states that if ab=0  then a=0 or b=0 We apply zero product principle while…

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Q: 5. ) If 3x + 4yi = Z2, what is x + y equal to?

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Q: 16 3. Show that for x2 + 2xy - 3y² = 4, y" (x-3y)3

A: We will find y" as following.

Q: Show for Re(z) > 1 -dr = r(2) ((2). %3D et - 1

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Q: Prove Formulas (1) - (9) Differentiate y = √3x². - 1 √5x = = (3x²)¹/³ – (5x)−¹/2

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