• Exercise 3 Prove that if S and T are both bounded linear operators from the normed space X to the normed space Y, then for all a E C and BE C the operator H defined by ÎĤ = aŜ + BÎ a) is a linear operator. b) is a bounded operator.

Q: If A is a square matrix such that A =1, then A'is equal

A: Given, A is a square matrix such that A2=I.

Q: One of the stationary points of the Uncuon Is this a maximum or minimum point of the graph?

A: Given: y=4x5-6x3+x2-2 The stationary point is (-1,1).

Q: [1 0 If A 2 -21 , then the matrix X for which 2X + 3A = 0 holds true is -3 4 -3 -올 3 3 6. -6 Select…

A: Find the matrix X for which 2X+3A=0.

Q: Given a scalar field f(x, y)= xy + x² and C is the curve defined by the equation y =-x². Calculate F…

A: Given scalar field  fx,y=xy+x2 and C is the curve defined by the equation y=-x2.

Q: -5 A = B = -6 0 -3 2 Compute -A + 3B. The result is equal to:

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Q: 2. Determine a basis for and the dimension of the solution space of the homogeneous system X3 + X4 +…

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Q: Define a sequence {E;} where En = r -,r| where n is positive integer. Find P({r}) for any r E [0,1]

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Q: 1 -1 2 -1 1 1 A = 1 1. 2. 1 1 3. 3 2 0. -10 0 -10 want -5 0 0. 2. B = 2 10 4 -5 -4 -2 From the given…

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Q: How much is the minimum cost for this assignment problem? 87 89 O 92 O 94

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Q: 9. Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R…

A: Since there is multiple questions, we will solve the first question. Repost the question again and…

Q: Express 7 (cos 300° – i sin 30°) in polar form.

A: convert in polar form

Q: Find all proper nontrivial subgroups of Z; x Z, x Z;. Find all subgroups of Z; x Z, of order 4.

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Q: 12. The graph of f is shown below on the xy-plane. Explain why y = 0.8(x – 1) + 0.4(x – 1)² + 0.1(x…

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Q: what is the argument f the Complex number -1-i ? a. 60° C. -45° b. 니7/3 d. -3 /u

A: Argument of the complex number

Q: f(t) = cos? 3t s2 +9 А. s(s2 +36) s2 +18 C. s(s2+36) s2 +6 В. s(s2 +9) s2 +18 D. s(s? +9)

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Q: 1-x 2 3 If 0 x 0 = 0, then its roots are: (a) 1 only (b) 0,1 (c) 0 only (d) -1,0,1 Select the…

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Q: Find the present value, using the present value formula and a calculator. (Round your answer to the…

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Q: x1 + 2x2 = -1 4x1 – 3x2 18

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Q: If the Wronskian W of f and g is t'e", and if f(t) = t, find g(t). NOTE: Use c as an arbitrary…

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Q: Consider the following two matrices: -2 -1 1 0) C = 7 -1 D = 3 3 -2 1 Which of the following four…

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Q: Using definition of Laplace transform, find F(s) if { 0 4. f(t) = e(1–2t)

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Q: On a garage sale, a hoodie jacket costs ₱795 after a 75% discount. How much is the original price of…

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Q: Which one is not equal to o V(x + 3)³ dx. lim, 100 E i=n-1 (음 + 3)3. O lima-00 1ri=n-1 Li-0 2i+1 +…

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Q: Find the surface area of a cylinder with a base diameter of 12 in and a height of 9 in. Write your…

A: To find the surface area of cylinder.

Q: if f(z) = (ax – x³ + 3xy³)+ (by – 3x²y+ y') is anal ytic , then the value of a and is

A: We have , f(z) = ax - x3 + 3xy2 + iby - 3x2y + y3 We have given that ,  f  is analytic function.…

Q: Find all proper nontrivial subgroups of Z; × Z, x Z;. Find all subgroups of Z; x Z, of order 4.

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Q: 5. Show that the functions x,x? -,x³ -x x are mutually orthogonal in the interval [-1,1].

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Q: [1 -1 A = 3 2 and B = 3, find (AB)T -1 5 1. 2. [-2 4] 3. 4. [-2 -4] Select the correct response: 1 4…

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Q: Use Gauss-Jordan Elimination to solve tl and the Gauss-Jordan Matrix (or Row Red ary of answers. 3x…

A: This is a problem of linear transformation.

Q: a, formula of the sequence:

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Q: f(x, 3) = In(x? + Y²òf function P(3,4) at the point of i = (9, 12) Directional derivative in the…

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Q: what Is the gimplest form of 5i (1-i) (2-i) (3-i) a. -10i -5/3 C. b. -8i d. -V½

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Q: Find the Fourier series of f(x) = {1 2<x<4 and f(x) = f(x + 4), and calculate the partial sums…

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Q: Using the theorem on determinants, show that 1 a a2 A = 1 b b2 = (b – a)(c – a)(c - b) 11 - с с2

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Q: Solve the equation xcosy dy+(x+2)siny dx=0.

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Q: Use Green's theorem to find the counter-clockwise circulation for the field V = 2xyi – 3x°yj, where…

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Q: Problem 13.1. Let X be a topological space; let A be a subset of X. Suppose that for each E A there…

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Q: 4n +1 5.

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Q: ft) = cos 2t + sin 2t + cosh 2t + sinh 2t 2s? (s+2) А. (s2 +4)(s2 -4) 2s? (s-2) С. (s2 +4)(s2 -4)…

A: We find the Laplace Transform of  f(t)=cos(2t)+sin(2t)+cosh(2t)+sinh(2t).

Q: 4. Determine the number of zeros of the function f(z) = 2z* – 2iz³ + z² + 2iz – 1 in the upper…

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Q: 5. Consider the vector space P2 along with the subspace, H = span {1+21°, 2. -ť,1-f} Use coordinate…

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Q: 3. Find the dot product of à = and B =. 4. Find the scalar product of P = 10î – 4f + 7k and Q = -2î…

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Q: Use the integration theorem to show that Cos nx 효(72-3a2) =D Σ(-1)”-1! -T <x < T n2 n=1 and sin nx…

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

Q: Find a basis for the vector space of all 3 x 3 diagonal matrices. 0 0 1 0 1 0 1 0 0 0 1 0 0 1 0 0 1…

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Q: by using the (graphical method) find the optimum solution of X1, X2 that the maximum Z=10X1+25X2…

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Q: 8 3 Find the Inverse Laplace Transform of 35²+12 2- 49 3 - sin7t+ -cosh (2t) 7 4 A. 4 - sin2t +-sinh…

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Q: 4. у + 2x &y(1) = 2. y3

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Q: 1. Determine the direction cosines and direction angles for à =

A: To find  The direction cosines and direction angles for the given vectors.

Q: f (t) = sin? 4t + cos? 4t 4+s А. s2 +16 С. s2 +32 В. s(s2 +16) D. s2+16

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Q: Suppose A and B are non-empty bounded subsets of positive real numbers. Define A·B = {r •y:x € A, y…

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