Find the best approximation to u = (3,-7, 2, 3) as a linear combination = (2,-1,-3. 1) and = (1,1,0,-1).

Q: Calculate F . dr, where C is the square of (1,1, 1), (–1,1, 1), (-1,–1,1) and (1,–1,1), with…

A: Let F→x,y,z=zex-yezi→+2cosy-xezj→+ex-xyezk→ and C is the square with vertices…

Q: Suppose that T : R2 --> R2 is linear, T(1,0) = (1, 4), and T(1, 1) = (2, 5). What is T(2, 3)? Is…

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Q: Suppose , t2, ., , are linearly independent. Prove that S is linearly independent where (a) S=…

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Q: Find the component of u along v. u - (-2, 4), v- (1//7, 1/v2)

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

A: Answer

Q: estimate parameters and draw CRD model.

A: let us take the given linear model  Yij=μ+αi+∈ij where i=1,2,3; j=1,2

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: The functions y1, Y2, . .. , Yn are linearly independent, if and only if W (y1, 32, ..., Yn)(to) #0…

A: If two functions are linearly dependent then the Wronskian is zero for every value of t.

Q: { (0,3), (0,1) is linearly independent in R? ylgn O Ins

A: The given vectors are  (0, 3) and (0, 1) To find whether they are linearly dependent or not

Q: 18 as a linear combination of a and y Express the vector v y.

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Q: Suppose ƒ(1, 2) = 4, ƒx(1, 2) = 5, and ƒy(1, 2) = -3. Find the linear approximation to ƒ at P0(1, 2,…

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Q: Find the linearization of f(r, y, z) = x + y² + z³ at the point (1, 2, -1).

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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: Use chain rule to find az at (u, v) = (1, 1) if

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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: 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: Is the set S linearly independent? Yes No

A: We have to find

Q: Compute Jx²z ds where C is the line segment from (0,6,–1) to (4,1,5).

A: The objective is to compute ∫Cx2zds where C is line segment from  0,6,-1 to 4,1,5

Q: 4. Prove that the vector given by (2xy -y')7+(2x²y-3xy² +2) 7 is a gradient. Also, find the function…

A: The solution are next step

Q: Find the linearization L(z, y, z) of the f(x, y, z) = 2,/z° + y° + z° at the point (1, 2, 3). %3D…

A: Consider the provided function, fx,y,z=2x3+y3+z3 At the point 1,2,3 find the linearization. The…

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: Find the linearization of f(x, y,z) = x + y centered at (8,4, 5).

A: Given:fx,y,z=x+y at 8,4,5Formula:Lx,y,z=fx0,y0,z0+fxx0,y0,z0x-x0+fyx0,y0,z0y-y0+fzx0,y0,z0z-z0

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

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Q: Determine whether u= (-1, 11) is a linear combination of x =(1,3) and y=(2,-1).

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Q: If u = x2 + 2x -y and v = - 2xy- 2y, then the vorticity vector is - 3yk 10 -yk 110 YK III

A: We have to solve given problem: Concept:

Q: 4. If possible, express t as a linear combination of u, v, and w. t = (2, 13, 5), = (1,2, 1), v = (-…

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Q: Defined byT (x, y, z) = (y+2z, –2x+y+2z, –3x– y+52), is diagonalizable.

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Q: what is the linear combination of  u⃗  and v⃗ ?

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Q: Find the linearization L(x,y,z) of the f(x,y,z) = 6sqrtx^3+y^3+z^3 at the point (1,2,3).

A: The linearization of a function f(x,y,z) at a point (a,b,c) is given by the expression;…

Q: Repeat Exercise 27 for the forces KX = (2, – 3) and KY = (- 2, 3).

A: The given two force vectors are, KX→=2,-3KY→=-2,3 When we find the addition of two vectors, then the…

Q: The gradient vector of the function f defined by f(x,y)= In(1+7x² +5y²) is equal to Select one: O…

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Q: In the xy plane mark all nine of these linear combinations: c[2/1]+d[0/1] with c=0, 1 , 2 and d=0, 1…

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Q: a. Is S = {v1, V2, V3} linearly independent

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Q: the set A = {2+x², 3+ 5x – 4x²} C P2(R) - -) Show that A is linearly independent.

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Q: Show that u = (a, b) and v = (e, d) in K? are linearly dependent if and only if ad – be = 0.

A: Solved below

Q: Find a nonzero vector u with initial point P(-1, 3, -5) such that u has the same direction as v =…

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Q: The functions y1, Y2, · . . , Yn are linearly independent, if and only if W (y1, 22, *. Yn) (to) # 0…

A: Consider the following differential equation, y''+pxy'+qxy=0

Q: Is Vector Y in the Column space of A? What is the solution set? Write y as an appropriate linear…

A: the vector y is in the column space of A is the system Ax=y is consistent 819-59-13108abc=123…

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

A: Given function: Using the formula of linearization:

Q: Consider the linearizable functions as follows. Find new transformed variables (rª, yª, Bor B as you…

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Q: Let v = and v3 1 for which values of S, v,, V2 , and v3 are linearly %3D V2= %3D indonondont

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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: If v1, ..., V5 are in R' and v3 = 0, then {v, V2, V3, V4, V5} is linearly dependent. %3D

A: Definition used: v1, v2, ..., vk is linearly dependent if there exist numbers α1, α2, ..., αk, not…

Q: A. If the grades of the students in linear algebra and vector analysis is set to be x and y…

A: Let us denote X as the grade of linear algebra and Y as the grade of Vector Analysis. A. Excel…