. Check whether the following set of functions are linearly dependent or linearly independent: i) {e cos2x, e sin 2x}

Q: Find the PDE that is satisfied the following function u(x, t) = e' cos(x) %3D

A: Given function,  u(x, t) = et cos (x)  To find the partial differential equation.

Q: Given pair of functions is (sin3x,4sin3x) O a. Linearly Independent O b. Linear O c. Nonlinear O d.…

A: The pair of  differentiable function is linearly dependent if the  Wronskian is zero and is linearly…

Q: Find the power of the following signal f(t) = (4 – cos t)Cos3t -

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Q: Find the maclauin's sesies for y= cos(%)

A: y=fx=cosx2 Differentiating with respect to x, we get f'x=-12sinx2 Again differentiating with respect…

Q: Eliminate B and a from the relation. x = B cos(mt + a) *+ 2wx = 0 O * + w?x = 0

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Q: 4. sinh 23x ,cosh 23x

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Q: Which of the following is linearly independent? (a) 2sin?x & 1– sin?x (b) 4e2* & e-2x (c) 3sec?x –…

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Q: Compute r'"(t) and r'(t) for the following function. r(t) = (cos 5t, sin 2t, cos 3t) r'() = (ODD

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Q: Show that u = x³ – 3xy? is a harmonic function and find a corresponding analytic function f(z) = u +…

A: To show that u=x3−3xy2 is a harmonic function and to find a corresponding analytic function fz=u+jv.…

Q: Differentiate the following function. r(t) = (3t e -,3t In t,t cos t) r'(t) = (OOD

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Q: Compute r' (t) and r'"'(t) for the following function. r(t) = (cos 4t, sin 3t, cos 2t) %3D

A: If, r(t) =<f(t),g(t),h(t)> , where f(t), g(t) and h(t) are differentiable functions,   then…

Q: 5. x sin 7x , x cos 7x

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Q: Let C be the unit square with diagonal corners at -1 – i and 1+i. Evaluate O f(z) dz, where f(z) is…

A: Let C be the unit square with diagonal corners at -1-i and 1+i.Evaluate∮Cfzdz,where fz is given by…

Q: Eliminate parameters A and B but not parameter C by differentiating x with respect to t. x=A cos…

A: x=AcosCt+B Differentiating wrt t, we get  x'=-ACsinCt+B Again differentiating, we get…

Q: Which of the following is linearly independent? (a) 2sin?x & 1 – sin?x (b) 4e2x & e-2x (c) 3sec?x -…

A: We have to choose linear independent  solution set

Q: Let F(t) = In ti+ cos(7t) j+ e-t k, G(t) = Vf i -j+ 7t k and p(t) = tan t (a) Find [G(p(t))]

A: Given: Ft=lnti+cos7tj+e-tk, Gt=ti-j+7tk, pt=tant for finding ddtGpt, first we find Gpt for that we…

Q: Find the value of a,b ∈ R ,so that the following sets of functions are linearly independent for all…

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Q: Show that cos A x e 2 *,x2 0. %3D

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Q: Let u > 0 be harmonic in R². Show that u is a constant.

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Q: Determine which of the following pairs of functions are linearly independent. NO ANSWER + 1. f(x) =…

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

Q: 1, sin?x, cos?x 2

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Q: Which of the following pair of functions is linearly independent? (a) e, e(*-3) (b) 4, sin2x+ cos2x…

A: Which of the following pair of functions is linearly independent?

Q: c) If f(x, y)= e" cos 2x, then show that = 0.

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Q: Determine whether the given set of functions is linearly dependent or linearly independent on the…

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Q: Eliminate B and a from the relation: x = B cos(wt + a)

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Q: 3. Use the definition of f* g to find t * cos(t).

A: As per bartleby guidelines we can only answer the one questions at a time please post the other…

Q: b) (e** cos z) =

A:

Q: j) h(x) = 3 cos² r – 2 cos(r²)

A: To differentiate the following function hx = 3 cos2 x -2 cos x2 We know that, differentiation…

Q: Show that the following functions satisfy C.R.E f(z) = sin z

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Q: Evaluate f(t) = cos?(t) = COS COS L{f(t)} %3D

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Q: 7. Which of the following sets of functions is linearly dependent on R[0,2″]? (a) {6, x, sin x} (b)…

A: See the details solution in below

Q: Let f(x) = e cosx, sx %3D 2. Express your answers in exact form. ElN

A: Inflection point occurs when the second derivative of the function equals to zero.

Q: F k d

A: Use conic section we can prove it.

Q: Verify directly that the relation y = C3 e cos bx + c4e sin bx satisfies the equation [(D – a)² +…

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Q: f(t) = et+1 cos t. f(t) = eat43/2_ f(t) = eat cos 3t.

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Q: Determine whether the given set of functions is linearly independent on the interval (-∞o, co). f(x)…

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Q: Use Part 1 of the Fundamental Theorem to simplify the following expressions.

A: To find the derivative of the integral, one need to use fundamental theorem of calculus, by…

Q: Given G(x, y) = e cos(x+y). Evaluate OG at

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Q: Compute r" (t) and r"(t) for the following function. r(t) = (cos 3t, sin 6t, cos 2t)

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Q: Let A E R²x2 be special orthogonal. Show that there exists & E [0,27t) such that COS O - sin o A =…

A: According to question,Given Matrix,A = cos ϑ-sin ϑsin ϑcos ϑ

Q: 15. Determine if the given functions are linearly dependent or independent. (Prove your answers) {e…

A: 15.  a) Given, e2x, 3x Now the Wronskian is, Wf, g=fxgxf'xg'x=e2x3x2e2x3=3e2x-6xe2x≠0 Since the…

Q: 2. sin 10x , sin 20x , sin 30x

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Q: The value of 'a', for which u(x, y) = xt + ax?y2 + y is a harmonic function, is

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Q: Find f. f""(t)  =Cos t

A: To Determine: find f Given: we have f''''(t)=cost Explanation: we have…

Q: Use Fundamental Theorem of Calculus to evaluate the following: d a) sin t dt dx

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Q: cOS x , tan x

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Q: Find y' of the following function using MATLAB y = sec(In(2M * x))e5x + cos(2Nx)

A: here we write the function in MATLAB and then by using the command  we can find the derivative of a…

Q: One of the following sets of functions is linearly dependent {e3x, e 3} {x², 2x²} { sinx, cos2x} O…

A: We know if the Wronskian of two functions is nonzero then they are linearly independent and if the…

Q: sin 10x , sin 20x , sin 30x

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Q: luate by Green's theorem F.dR where F= -xy (x i-y j) and C is a (1+ Cos O).

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.