Let A, Be Mnxn (F). (a) Prove that if A~ B, then At ~ Bt.

Q: Let (a, b) belong to Zm ⨁ Zn. Prove that |(a, b)| divides lcm(m, n).

A: Given: a, b∈Zm⊕ZnWe need to prove that a, b divides lcmm, n.

Q: Prove that RXY (T)l S V[Rxx (0) Ryy (0)].

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Q: 71. Let z = (f(x, y))". Show that az n(f(x, y))"-1 and af az = n(f(x, y))"-1ºJ ay ax ax ay

A: Given: z=fx,yn Partially differentiate the function with respect to x, using chain rule.…

Q: If α < α', show that Dα'f⊆ Dαf .

A: Let's assume that α and α' are constants such that α<α', and let f be a function that is…

Q: We defined NCE) = ZE for ZE Z Ii]. Prove N (Zw) = NLZ) Ncw) for all Z,W E Z6] .

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Q: O det f: (24, Q) → ( % -103, O) be a funchon defi'ned bey Ho)= 1, fi) = 2, f12)2 4 and f13)=3. Prone…

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Q: a) Cov (a X , b Y) = ab Cov (X, Y) b) Var (aX + bY) = a2. Var (X) + b2. Var (Y) +2 ab Cov (X, Y)

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Q: A given that PCA) = 0.4 and B p(B) = 0.3 P(A/B) Hint: PCEUF) - PCE) + PC.F) - PE/F) = PCENF) P(F)…

A: According to the question, we have to calculate P(A|B). Conditional probability : If A and B be two…

Q: Q.1B) If w = f(u,v) where u = tan"12 &v=In(x² + y²), the show that: dw Х- +- дх дw dw <-2- ду ду

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Expand [× (à × ř)] d dt

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Q: Since Cov (X, Y) = E [X, Y] -E [X] E [Y]. Obtain Cov (Yi, BO)

A: From the given information, Consider, the regression equation be assumed as given below:…

Q: |7| = r Eya f(r) gř = 5xi + 2yj – 2zk il Jligull %3| div) grad(f) ja JS da

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Q: O 2 0 [o 0 1 0 0 -1| B = |1 0 0 1 0 | 0 1 1 a) Write down AT and BT. b) Calculate AT BT. ||

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Q: Let and ond let F:Co, a) -R be a quactien that is and q =3 dipperenhable on Coja), and such Hhat…

A: To solve the following problem and find F(3)

Q: 2. Prove: a. [(x)b~ XE]~ = (x)b XA b. Эх (~p(x) A ~q(x)) = ~[Vx(p(x) V q(x))] 3 Dariva

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Q: (18) Find [S], where S = {(a, b, c)|a, b, c E [100], a <b, a <c}.

A: Here is how the set S is defined: S = {(a, b, c) | a, b, c ∈ [100], a &lt; b, a &lt; c}   We must…

Q: Let X+5x+4. Examine whether the given polynomidl is irreduable over the QUI, ZCXJ, CIX).

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Q: exemple where cxiste Iab] Grve an g though f s unbanded a even

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Q: Prove that (A O B)/(A Ð {e})~B.

A: We need to prove that A⊕BAA⊕e≈B To prove that A⊕BAA⊕e≈B, we need to show that there exists a…

Q: let f={ Ca,b) : a,bGR 3 and +,. defined on F as (a,b) + ( Cd)- (arr, bod) vla,b).(c,d) Ef Pollous:…

A: f=a,b : a,b∈Rg:f→M2×2 defined asga,b=ab00 , ∀a,b∈F

Q: Let X, Y subset U. Suppose that n(X)= 22, n(Y)= 20, and n(X intersect Y)= 16. How many elements are…

A: Let X,Y be subsets of U.  nX=22 , nY=20 and nX∩Y=16 It is given that nU=40. Find nX'∪Y:

Q: 2. Prove that a) A(BC) = (AB)C b) (AB)¹ = BT AT

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Q: R and r are defined by E(; - 1)(y, – I) VE(*; - 1)² E(Y SSR Sry S,, Syy R? TY r = SST' (1) Show R2 =…

A: Given : R2=SSRSSTr=∑xi-x¯yi-y¯∑xi-x¯2∑(yi-y¯)2r=SxySxxSyy

Q: 2) Let u(xy,2) = でさす。R。 () Find He(tいり, "g(1,0,り、 Uy(1,0,1). ニ0. (k) Show that oty a22

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Q: It G acts set tdansikivey then show that y Salgdnap Hof 0n A by to the actioh af en A fusthus then…

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Q: Prove Va e Z, Vb e Z, 3|(a² + b² ) – 3|a ^ 3|b where xy means x divides y, i.e., there exists k e Z,…

A: In this question we use congruence modulo.The following  are useful in this question1) If  3 |…

Q: Problem (3) Discuss the Discuss the unif Conv. (a) Ž 22², A= (0,0) n=1 12 (b) sin(x²); A = R 8 کے…

A: As per the policy,  we are solving three parts. Please repost it and specify which part is to be…

Q: Let X ~ NB(r, p). Show that E(X*) =-E(Y – 1)*-1 where Y ~ NB(r+1, p). а. b. Use this result to find…

A: It is given that:

Q: In AABC andAXYZ, AB = AC = XY, BC =Y Z and mZZ = 90. Prove: mZX > mZA %3D

A: We have given two triangles , ∆ABC,∆XYZ and AB=AC=XY and ∠Z=90∘ . and BC=YZ We have to prove that…

Q: Prove that (S ⋂ T)c = Sc ⋃ Tc and  (S  ⋃ T)c = Sc ⋂ Tc .

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Q: @ Let A -a Find Cenditiens on a,b.c and d that AX =o has infailely many Solution. what must there…

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Q: Q4. Let A E Rnxm, n ≥ m. a) Use the SVD of A to deduce the SVD of ATA. b) If m = n and A is…

A: Given: The given expression is, A∈ℝn×m , n≥m a) To use the SVD of A to deduce the SVD of ATA b) To…

Q: End (Z₂Zp) = M₂( Zp) (Verify).

A: Endomorphism Ring (End(A)): For an abelian group A,End(A) is the ring of all endomorphisms of A.An…

Q: Let S={(x,y)∈N×N|(2−x)(2−y)<2(4−x−y)}.Prove that S=TS=T, where T={(1,1),(1,2),(2,1),(1,3),(3,1)}

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Q: . d the しいwits UI- Vタ+1 ユ ーリー! Cスリ る) しm 5) (Z,y)>(,) Cos Tzyl-a C)にm 反- vy Ca,y)Co)

A: Consider the limits, To solve, Multiply by the conjugate of numerator,

Q: Find a norm of the function flt)= t+2t in space C^co13 %3D where normis given by formula ms x…

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Q: Let f(r, y) = In (z³y) (1,3) = 3. then Select one: O True O False

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Q: Let o e C (RN), he RN - (0}. For teR', we set (r+th)- (x) (x) 1- Show that e C (RN).

A: Since, you have post multiple question. I am answering first one. Please post again for the…

Q: If the column space of A is C(A) = R", then det A +0. %3D O a. TRUE O b. FALSE

A: The solution are next step

Q: Prove z = max (x,y) and z = min(x,y) are convex

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Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.