In C[0, 1], are the functions {x2 , x3 , e2x} linearly independent?

Q: Express ax? + bx + c as a linear combination of the functions f(x) = 4, g(x) 2x, and h(x) = -x²,…

A: Sincewe can write every element of P2 in linear combination of f(x),g(x),h(x) so this functions…

Q: find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = x3 - 2x + 3, a = 2

A: We find f(x) and f'(x) at x=2

Q: The linearization at a = 0 to v8 + 5x is A+ Bx. Compute A and B. A = B = ||

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Q: Show that ex and e−x are linearly independent in C(−∞,∞).

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Q: Find the linearization L(x) at x= a. f(x) = x+ a = - 1

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Q: Is {x² – 2.x, x²+x, x²} linearly independent dependent? Prove your answer. or

A: Answer

Q: Determine whether the functions f1(r) = e2*, f2(x) = e-2" , and f3(x) = sinh 2x are linearly…

A: To determine whether the functions f1x=e2x, f2x=e-2x, and f3x=sinh 2x are linearly independent on…

Q: The linearization at a = 0 to /3 + 9x is A + Bx. Compute A and B. A = B =

A: Given: f(x)=3+9x

Q: Find the linearization at x = a. f(x) = 6x®, a = 1

A: Linearization L(x) of function f(x) at a is given as L(x) = f(a) + f'(a)(x-a)

Q: Show f(x) = e and g(x) = xe linearly independent by finding its Wronskian.

A: Given: fx=exgx=xex The formula to obtain the Wronskian is Wx=f(x)g(x)f'(x)g'(x), where f(x) and g(x)…

Q: Find the linearization of g(x) = 3 + sec (t - 1) dt at x = -1.

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Q: 35. Give linearly independent functions that are annihilated by D² (D² – 2D + 10).

A: We will find roots for the equation and use concept of differential equations to find the linearly…

Q: Find the linearization of f(x) = 9 – dt at x = 1. 2+t

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Q: The set of functions {Vx, x, x²} is linearly dependent on (0, oo). True False

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Q: find the linearization at x = a. f (x) = x4, a = 1

A: Given function: Using the formula of linearization of a function f(x) at x =a :

Q: [2] Show that the functions f (x) = 4x" , and f,(x) = x*+* linearly independent (-00, 00). are on

A: To Show: Show that the functions f1x = 4xn, and f2x = xn+4 are linearly independent on -∞, ∞…

Q: Show f(x) = e2= and g(x) = x e²z linearly independent by finding its Wronskian.

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Q: If after evaluating the Wronskian of the functions y1 and y2 the result is W=7x2+19 in the interval…

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Q: 2. Find the equation of the linear function z = c+mx+ny whose graph contains the points (0,0, 0),…

A: We solve only one problem at a time so please submit them one by one for fast and thorough answers.

Q: If f* f(t) dt O 6 1 O -4 divergent = 20x √4x²+21 ∞ -4, then f(t)dt is X

A: Given

Q: The function f(x) = Ei-1 Cix;| is piecewise linear and convex. True O False

A: Step:- 1 Convex piece-wise Linear: - A function f: ℝn→ℝis a convex piece-wise linear if there exist…

Q: Show that the functions e*, cos x, and sin x are linearly independent using the Wronskian.

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Q: Show that the functions e^x , e^2x , e^3x are linearly independent.

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Q: In x Find the linearization of f(x) = xmª around x = e. Round the gradient and y-intercept, whenever…

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Q: Let Dy be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: The linear transformation Dx:C'a,b→Ca,b maps a function fx to its derivative Dxf. Here, given that…

Q: The functions y1, Y2, . .. , Yn are linearly independent, if and only if W (y1, Y2, ..., Yn)(to) # 0…

A: We can use the Wronskian test to check the functions are linearly independent or dependent.

Q: Determine the linear approximation of f(x) = =ª at æ = 1. O a. y=- 4x-3 O b. Not in the list O c. y=…

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Q: Find the linearization L(æ) of y = (81+ 2æ²)-1/2 at a = 0. L(x) =|

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Q: Determine if the functions Y1=e^{4x}senx and Y2=e^{4x}cosx are linearly independent or linearly…

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Q: The functions y, = e* – e-X a y2 = - 3ex + 2e-x are linearly independent. True False

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Q: Consider x1 = et and x2 = v(t)et. If x1 and x2 is linearly independent, then v′(t) = 0. Is this…

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Q: Eliminate the arbitrary constants a. x = -In t, y = at + bt?

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Q: Find the linear approximation of the function at the given point. f(x, y) = -4x²y³ at (-9,7) O A.…

A: In this question we have to find linear approximation of the given function.

Q: find the linearization at x = a. y = (1 + x2)^−1/2, a = 0

A: We find the derivative of the given function using power rule and chain rule

Q: 5. Determine whether the functions y, and y2 are linearly dependent on the interval (0,1). Yi = 1+…

A: Linearly independent of the function. Using Wronskian

Q: By direct differentiation of x(t) = eAtxo + eA(t-o) Bu(o)do show that ¿(t) = Ax(t) + Bu(t), x(0) =…

A: The differentiation of a definite integral can be obtained by using the Chain Rule following…

Q: say f(3)=5, f'(3)=-2 and let g(x) =xf(x/2) find the linearization of g(x) at x=6

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Q: Which set of functions which is not linearly independent is  A-X^2,4x^3 B-2x,6x+3,3x+2 C-e^x,e^2x…

A: A set of functions will be linearly independent if there Wronskian is not equal to zero. Wronskian…

Q: 1. Use the Wronskian to show that the functions are linearly independent. Yı = e*, y2 = e2*, y3 =…

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Q: Suppose that , g(t) dt = v2 g(t) dt 1. g(u) du 2.

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Q: Suppose f(x, y)= g(x)h(y), where g and h are continuously differentiable functions of one variable…

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Q: find the linearization L(x) of ƒ(x) at x = a. ƒ(x) = x + 1/x, a = 1

A: Given fx=x+1x

Q: Let D, be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: Dx(f)=8x+5 Apply integration both side  ∫Dx(f)dX=∫(8x+5)dx   f(x)=(8x2)/2 + 5x +c (here c is the…

Q: Show that the functions f1 (x)=e*, f 2 (x)=xe*, and f 3(x)=x*e* are i linearly independent.

A: We will use Wronskian function to check these functions are linearly independent or not. we know…

Q: Obtain the function x to minimize the following functional. 1- J = , (0.5x2(t) + 3x(t)x(t) + 2x²(t)…

A: Given functional is J=∫010.5x.2(t)+3x(t)x.(t)+2x2(t)+4x(t)dt with x(0)=0, x(1)=4 Here…

Q: find the linearization at x = a. y = e√x , a = 1

A: Given function: Using the formula of linearization:

Q: Show that the functions ƒ 1 (x) = sin x, ƒ 2(x) : = cos x, and f 3(x)=x cos x are linearly…

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Q: Find the linearization L(x) of the function at a. f(x) = e5x, a = 0 %3D L(x) 1 + 5x

A: f(x)=e5x point a=0

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.