0. Let v is v linearly independent or dependent? O Independent O Dependent

Q: zow(t)dt = zo / w(t)dt. 2. a. [w(t) + W(t)]dt = | w(t)dt + | w(t)dt 3.

A: The general formula for the integration is I=∫abf(x)dx. Here, a is the lower limit and b is the…

Q: Find the linearization at the point indicated:   V (h) = 4h(2 − h)(4 − 2h), a = 1

A: Given: Vh=4h2-h4-2h ,a=1

Q: if was T!R R? Linearidentifir grandfather OkerT ImiT

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

A: Answer

Q: Suppose v, w e R" and {v, w} is linearly independent. Prove that {v – w, 2v+w} is linearly…

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Q: Let v =| 0 V2= S, and v3 for which values of S, V,, Vz, and v, are linearly independent. Select one:…

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Q: Write v as a linear combination of u and w, if possible, where u = (1, 2) and w = (1, −1). v = (−1,…

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Q: 3 For which value(s) of h is the set 4. -8 linearly 1 7 independent? Write your answer in one of the…

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Q: { (0,0,0), (3,5,6)} is linearly dependent in R' ulgn O ihi O

A: A set containing the zero vector (0,0,0) is linearly dependent.  Therefore the given set {(0,0,0),…

Q: d [u (v X w)] = dw. lu • (v X w)] = [v X w]+ u• xw] [v X w] +u * + u * [v X dt dt dt Idt

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Q: ) Let B = {vi =,₂ =, V3 =}. Determine whether B is linearly independent or linearly dependent.

A: Let us consider a set of vectors V=v1,v2,.......vn. The set of vectors are said to be linearly…

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

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Q: For what values of h is v3 in span {v1, v½} and for what values of h is {vi, V2, V3} linearly…

A: Given vectors  V1=133 , V2=39-1, V3=-2-6h 1) V3=Span{ v1, v2} 2) V1,V2,V3 is linearly dependent.

Q: Are the functions f(x) = e ^x and g(x) = e ^|x| linearly independent on I = (−1, 1)? Are they…

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Q: assume thatf (2, 3) = 8, fx (2, 3) = 5, fy (2, 3) = 7 Which of (a)–(b) is the linearization of f at…

A: Consider the given: f2,3=8fx2,3=5,fy2,3=7,

Q: a 6) Determine the value(s) of a such that is linearly independent. a +

A: Let us consider the n vectors of order 1x n in Rn  The vectors are said to linearly dependent if the…

Q: Which of the following sets is linearly independent?" {C 16 3 the above set the above set

A: The set is linearly independent if the elements cannot be written as a linear equation. Thus, if the…

Q: Is the set S linearly independent? Yes No

A: We have to find

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

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Q: The set of all linearly independent solutions of D.E yY-y 0 is Select one: a. (1,t,e',e ) b.…

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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: Write v as a linear combination of u and w, if possible, where u = (1, 2) and w = (1, −1). v = (1,…

A: Given u=1,2 and w=1,-1 , v=1,-4we write v is a linear combination of u and w if possible .

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

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Q: {(0,0,0), (3,5,6) ) is linearly dependent in R ulgn O İhi O

A: Given {(0,0,0),(3,5,6)}

Q: Prove that if {u, v} is linearly independent, then so too is {u+ v, u - v}.

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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: Differentiate the follo ear and non-linear. w +z =2 1. x +y- z= G X +v-

A: (i) First we differentiate the given equation with respect to x: xy+z=2⇒ddxxy+z=ddx2⇒y+xdydx+dzdx=0…

Q: Write v as a linear combination of u and w, if possible, where u = (1, 2) and w = (1, −1). v = (0,…

A: Here u = (1, 2), w = (1, -1) and v = (0, 3) Since v is a linear combination of u and w So consider v…

Q: Are fi (x) = x, f2(x) = x², and f3(x) = 4x – 8x2 linearly independent or linearly dependent on (-00,…

A: Definition: A set of vectors are said to be linearly independent, if no vector can be represented as…

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

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Q: Express w as a linear combination of u and v. 1 - 5 u = V: w = - 9 w = u+

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Q: Suppose v1, ..., Vm is linearly independent in V and w e V. Prove that if vi + w, ..., Vm +w is…

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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: For which value of x do the following vectors form a linearly dependent set in R V =| x, x,

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Q: 6. If u = given by x = +2, where x+y+z= 1, prove that the stationary value of u is y b a+b+c' a…

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Q: Prove: If ū and v are linearly independent, also au + bü = cũ + dủ, then a=c and b=d. %3D

A: Introduction: Two vectors u and v are linearly independent, if there exist two scalars such that,…

Q: Let r E R and --(), v- (), -- (1). 3 u = V = W = 2 For which values r ER is the set {u, v, w}…

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Q: Check the set 4 2 3 Mas(R) = 11 is linearly dependent or linearly independent

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Q: a 6) Determine the value(s) of a such that is linearly independent.

A: Given the set 1a,aa+2 is linearly independent.

Q: If W(f, g) = sin t then the functions f, g are linearly independent Select one: O True False

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Q: Consider the model Y; = Bo + B1 X1,j + B2 X2,i + u¡ where X2,i is not observable. However, you have…

A: There may, sometimes, be errors in measurement of variables. The variables are then said to be…

Q: Evaluate fcF. dr where F = ( 3 z – y)i + (2 x +2 z)j + 2 z k along the straight line from (1,1,2) to…

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Q: The Wronskian has been computed. Determine whether the functions are linearly independent or…

A: Here given the wronskian of function ex and 2ex is zero.

Q: O let )ارارا ره( - V Vz = (i) show linearly independent if that )اراواو 2 - V is set generated by…

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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: Which of the following is/are linear function(s) of x, y, z? A. x - z V2 + y В. Зх — 2тIz С. Зx2…

A: To find the linear functions of x, y and  z.

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…