Decide whether (t) = t + 3, 2(t) = t² – t, 3 =t + 3 are linearly independent or linearly dependent. In the latter case find a linear relation among them.

Q: 2. Given T: R² → R² is a linear operator such that T (H) =3] Is it possible to determine T ()? If…

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

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Q: Find the linearization of ƒ(x, y) = x2 - xy + 1/2 y2 + 3 at the point (3, 2).

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Q: Let f (x, y) = (x − y)e^x . Use the Chain Rule to calculate ∂f/∂u and ∂f/∂v (in terms of u and v),…

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Q: 5|, B= -14|, and C = |2 2 -11 B and C linearly dependent, or are they linearly independent? -arly…

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Q: Show that the functions f, (x) = 4x" , and f2(x) = x"** are linearly independent on (-00, 00).

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Q: Find the linearization of ƒ(x) = 2/(1 - x) + √(1 + x) - 3.1 at x = 0.

A: Here The formula for the linearization is Here a = 0 Therefore,

Q: (d) Show that the function T: R2 - R? defined by T(Vi, v2) = (vi-v2, vi +2v2) %3D is a linear…

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Q: Given the function T:R²→R³ defined as X2 2x2 – X1 4x1 | i) Show that T is a linear transformation.

A: To show that T is linear transformation, where:

Q: Is T linear? If Yes find KerT, where T(x1, x2, x3) = (x1+x3, x1-x3, x2 )

A: Given Tx1,x2,x3=x1+x3,x1−x3,x2 We have to show that T is linear and then find the KerT Let…

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

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Q: The functions y1, 2, ..., Yn are linearly independent, if and only if W (91, 32, ..., Yn)(to) #0 for…

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Q: Let T : P2 → P2 be a function represented by T(c + bx + ax2) = (3c + a) + (2b + 3a)x + ax2 Determine…

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Q: If ů, = |8|,02 = 5,03 show that {v1, v2, v3} is linearly dependent in R', and determine the linear…

A: Letv1=2i^+8j^+3k^v2=i^+5j^+2k^v3=i^+j^Let…

Q: Use the chain-rule and find x and y in terms of x, x, and if:

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

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Q: r([L1, T2]) = [2x1 – #2, T1 + ¤2, T1 + 3x2]

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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: Suppose that S = {v} is a linearly dependent set. What is v?

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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: Find all values of h such that {t² + 2,5t² + t - 7,-4t² - t + h} is a linearly dependent set in…

A: We are given a set of 3 polynomials in polynomial space P2[t] , including a unknown parameter h And…

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: :R3-R3 defined by  T(x,y,z)=(x,y,0) Show that T is linear and find its range and kennel

A: T : IR3→IR3 defined asT (x,y,z) = (x,y,0)Let (x1,y1,z1) , (x2,y2,z2) ←IR3 and ⋉←IR ThenT…

Q: 1. yı(t) = 2t – 3, 2(t) = t² + 1, y3 = 212 - t %3D 2. y1(t) = 2t – 3, y2(t) = 12 +1, y3 = 212 – t,…

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Q: Which of the following sets is linearly independent? -ex-y-5=x+C OM= {(1,3),(3,9),(-1,-3)) M=…

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Q: Show that the functions y1= e^t,  y2 = e^-t, and te^-t are linearly independent.

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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: Determine whether the function is a linear transformation. T: R2 - R2, T(x, y) = (x, 8)

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Q: Determine if the set of functions {e* , xe* , x²e* }is linearly independent or linearly dependent. O…

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Q: Consider the functions f(x, y, z, t) = (x² + 2. t²) and g(u. v) = (uy, u +v. u – v). Use the chain r

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Q: Verify whether u = x+y+2, v = x²+y² +z², w = x³+y³+z³-3.ryz are functionally dependent, and if so,…

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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: Find the value of x so that the following are linearly dependent in R³. (1, –1,0), (-1, x, 0), (0,2,…

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Q: Let r (t)= - The x component of r' (-1) =

A: r'(t)=<2t,3,5> r'(-1)=<-2,3,5>

Q: which of the pollowing sets contain functions that are linearly independent ? C3x (3x -1 x+2, 4x) a.…

A: We have to find

Q: If the function f(x, y) = ;x³ + y² + 2xy – 6x – 3y + 4 has one saddle point (a, b), then 46 + a = -

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Q: Determine whether the following are linear transformationsfrom R3 into R2. L (x) = (0, 0)T

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Q: 3. Determine whether the functions e and re are linearly independent or dependent by calculating…

A: f= {e^2x , x.e^2x} is Linearly independent if Wronskian is non zero.

Q: Let Tv = Av represent the linear transformation T: R2 → R3 where 1 2 A = -2 4 -2 2]

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Q: Write the expression for a linear transformation T: R2 → R?. whose null space be the straight y=3x

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Q: Show that the functions f (x) = |x + 1|and g(x) = x² are linearly %3D independent on the interval I…

A: Given that f(x)=|x+1| So, f(x)=x+1 in [1, ∞) g(x)=x2

Q: Suppose that T = f(t) gives the temperature T (in degrees Fahrenheit) of a pot of coffee t minutes…

A: Let  T=f(t) be the temperature(in degrees Fahrenheit) Given  f'(20)=-3 and f(20)=125 we have to find…

Q: Show that {x, y} is linearly dependent if and only if x or y is a multiple of the other.

A: It is given that, x and y are two distinct non-zero vectors.

Q: Let T : P2 → P2 be a function represented by T(c+ bx + ax?) = (3c+ a) + (2b + 3a)a + ax? Determine…

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Q: Determine whether the following are linear transformationsfrom R2 into R3. L (x) = (x1, 0, 0)T

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