Let linear tiansformation I(4)=(2,32and Tls0) =(3B,2) Cheek whether T? exists or noti2 Find T. E=R andT:R R? be a Such Aat

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Q: Let {X;} be i.i.d.~ Exp(0) and a; > 0. Denote by Z = min{a,X1,..., amX,}. Suppose that 0. Prove that…

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Q: 6. Suppose that {a,} satisfies the hypothesis of Leibniz's Theorem. Use the proof of Leibniz's…

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Q: 1- iz If z = x +iy and w =- z-i show that w = 1= zis purely real

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A: Given, Let z=f(u,Y) u=ax+byY=ax-by

Q: The linearization a at a = 0 to √8+7x is A + Br. Compute A and B. A B=

A: To Find: Linearization for fx=8+7x at a=0

Q: If TeZx Such that x is a momber of 27+5x-3=03 and S={x Such that x i. member of 2i+71+233/3 that T…

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Q: Letr(t) = (t2, 1- t,4t).Calculatethederivativeofr(t) • a(t)att = 2, assumingthata(2) = (1,3,3)…

A: Given that, rt=t2, 1-t, 4t a2=1, 3, 3a'2=-1, 4, 1 Need to evaluate derivative of rt.at

Q: 10 6) Let g(x) =+ 3 %3D x2 Is g(x) E [3,4], Vx E [3,4]?, using fixed point theorems what can you…

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A: we have to show that given function is bijective

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Q: Let, T:R' → R³;T(x,y,z)=(2x+ y, y- z,2y+4z) 2. Find the rank and nullity of T.

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Q: A) Show that the surtace x-2yz ty' =4 is orthogon al to any of the sm tamily of sur faces…

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Q: Drag the postulate or theorem that proves the trieng AZWX AY XW a. ATSU AXVW # SSS E SAS

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Q: Let E=RandT:R R be a Linear tiansformation I(,)=(2,3)and Tls0)=(3,2) Check whether T exists or noti2…

A: Given T:ℝ2→ℝ2 is a linear transformation such that T1,1=2,3 and T1,0=3,2. Now find the matrix of the…

Q: Let z = ƒ(u, y), u = ax + by, and y = ax - by. Express z x and zy in terms of fu , f y, and the…

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Q: Given that vec F =x^ 2 y hat i -(z^ 3 -3x) hat j +4y^ 2 hat k find the k- component of ( nabla* vec…

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Q: 2 Given t = -1 and U = -1|, for which is the set {u, T, w} {d, v, 2 linearly independent?

A: Given that, u→=1-12 and v→=2-11 We have to find the vector w→ for which the set u→, v→, w→ is…

Q: Q1) Use a suitable Linearization to find the best fit of the form f(x) = Cx3 + for the %3D data:…

A: Given the data,                 (1, -1), (2, 7), (3, 26.3)

Q: Prove that if a e R, then a 0 = 0 = 0 · a. Suppose x, y, z E R. Show that xz = yz if and only if…

A: We will prove the given statements.

Q: * Let A E R"Xn, ĩ E R" \ {0} and A = 0. Prove that if the origin is stable if and only if ī is…

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Q: Let X; ~ X"(1) i= 1,2, . - ·, n and assume they all uidependent are Y = Ź Xi %3D しニ」 ان منتتفينتمنل…

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Q: In R, the model mod <- Im(z ~ x + y) will contain: O the results from regressing the dependent…

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Q: EX: Find the Z. T. of X(X) = cas wok u(k) 8 iwok -iwok Sol:- X(Z) = - IN Σ coswok. Z k=o == {(² z ¹²…

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Q: 5. (a) Make a tree diagram for the chain rule for f(x, y, z) = x²y² + y²z² + x²z², x = rt, y = r²t³,…

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Q: Suppose X1, X2, and X3 are independent and N(0.1)-distributed. Com- pute the moment generating…

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Q: (2) Let P = (1, 1), Q = (4, –2) and R = (2,3). Find the point S such that R$ is equivalent to PQ.

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Q: 1. Let TE L(V) and suppose v is in the range of T and w is in the null space of T". Show explicitly…

A: To solve we will use the definition of adjoint operator.

Q: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

A: Prove that if A−1exists, then there can be no nonzero y for which Ay = 0.

Q: (a) Show that for p> 1, |æ1|P + • .· + |æn|P f(x, t) = tp-1 tp-1 is convex on {(x, t) | t > 0}.

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Q: Which of these best describes T?

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Q: 8. [M] Show that {1, cos t, cos? t,..., cos t} is a linearly inde- pendent set of functions defined…

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Q: LZHP - DTNV. Complete the statement below. ZZ = _2_

A: Consider the following condition: LZHP~DTNV Hence, ∠L≅∠D∠Z≅∠T∠H≅∠N∠P≅∠V

Q: The linearization at a = 0 to √8+7e is A + Ba. Compute A and B. A B= || ||

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Q: 2 2) Find a number t such that -3 is not linearly independent in R.

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Q: Which of the following is a nonlinear second order nonhomogenous PDE a. xux-Uxx=tuxt O b.…

A: To find - Which of the following is a nonlinear second order non-homogenous PDE x ux - uxx = t uxt…

Q: 1. Let z, y € R" be given. (a) If ||z|| = ||y|| = 1 and z-y = 1, show that z = y. (b) If ||z|| ≤ 1…

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Q: ☺ RB=R defuid by T☺)- matria "A" it. T@)- A:). つレ- TV4 Let T: -3v-Jw ). Füd

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Q: 7.18 Show that the fitted regression plane ŷ = a + B₁(x₁ - passes through the point (x₁,x2,..., xk,…

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Q: Determine the quadature rule of the form | f(r) dr = Aof(ro) + A1f(£1) + - *·+ Anf(Tn) a. when the…

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Q: Find all the values of x satisfying the given conditio

A: Given:- y=x-√(x-2) To find:- value of x when y=4

Q: If F G) and g(x) are conbinuous on [anb] andit =Sprove thab. SF= 58 prove thab Icefanb] Such that…

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Q: Suppose that T :C C is R-linear. Show that T is C-linear if and if T(iz) = iTz for all z.

A: First we describe the definition of C-linear function:

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Q: 3. C-1) " Conditionally absolutely codvergent divergent. Con vergent, 2n+ Sinin) or

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.