Show that if S={v,v2,V3} is linearly independent and v, is not in Span{S}, then {V,V2, V3, V43 IS linearly independent.

Q: let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove that…

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

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

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Q: ) Let B = {v₁ =, V₂ =,v3 =}. Determine whether B is linearly independent or linearly dependent.

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Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent.S = {−2 −…

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A: Given, {1, x, x2, ... , xn}

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A: We have to find the given vectors are linearly independent or dependent  Here year I am solving…

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A: Here given that                        u=213 , v1=13  and v2=2-1 Now we determine that u=213 is a…

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: 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: Prove that if T:V-oW io a one to-one linear trans formation and 33 o a linearly deperdent then…

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Q: Determine whether the set {P1, P2, P3} is linearly independent in P2, where p₁ = 2+x+3x² + 4x³, p₂ =…

A: Let V be a vector space . let v1,v2.....vn ∈V are linearly independent iff c1a1+c2a2+...+cnan=0…

Q: Prove that if {Vi, V2, v3} is linearly independent, then so too is the set {u, u2, u3 where u = V -…

A: Introduction: Linear dependence and linear independence of a given number of vectors are very…

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Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent.S = {2 − x,…

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Q: In each part, determine whether the vectors are linearly independent or are linearly dependent in…

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

Q: In each part, determine whether the vectors are linearly independent or are linearly dependent in…

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Q: Suppose we have a set of vectors v_1...v_n such that v_1 could be written as a linear combination of…

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Q: Determine whether the set [p., pa, p3] is linearly Independent in Pa, where pi= 3+x+3x²+4x3 Pa = 4+…

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Q: Prove that the intersection line of the planes P₁: 2x -y - 2z = 0 and P₂:x-2y+z = 0 is parallel to…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

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

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Q: Given any linearly independent set of vectors V = {v, V2, , }, prove that there is at least one…

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

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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: Find the norm of x and the unit vector ü in the direction of x if ||| = u =

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Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

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Q: "Span(u1,..., in) = Span(71,..., Tn, w) if and only if J1,..., Un, w are linearly depen- dent."

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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: (b) By determining constants c,, C2, C3 and c4, which are not all zero and are such that cifi(x) +…

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Q: The vector v, is in Span{ v2,., Um } if and only if ( v1,., Vm ) are linearly dependent. O True O…

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Q: Determine whether the set {p1,p2,p3} is linearly independent in P2, where p1 = 2+x+3x^2 +4x^3, p2 =…

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Q: suppose that x,y,z∈R3 are such that x.(y×z)≠0. prove that x,y,z are linearly independent.

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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: Prove that if (V1,V2, V3} is linearly independent, then so too is the set (u,u2, u3} where u, vı-…

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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: Suppose vi, v2, ..., m is linearly independent in V and w ɛ V. Show that v1, vz, ..., Um, W is…

A: v1, v2,......., vm is linearly independent in V and w∈V

Q: Show that t, e^t, and sin(t) are linearly independent.

A: In the given question we have to show that t, e^t, and sin(t) are linearly independent.

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Q: Show that the set {1, x, x2, ..., xn} is linearly independent in Pn(F).

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

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Q: The vector v, is in Span{ v2,., Vm } if and only if ( V Vm ) are linearly dependent. O True O False

A: Check is it dependent or not

Q: Let S = {v1,v2, V3} be a linearly independent set of vectors in {u1, U2, U3}, where u̟ = vị + v2 +…

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Q: Given the functions 2x and |x|, show that (a) these two vectors are linearly independent in C[−1,…

A: (a)  The linear combination of two given functions is  2xc1 + xc2 Now , put x=1 and -1, we get two…

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: Consider the collection of vectors {v1, v2, V3}, where v1 = -3v2 + 7v3. Is the collection linearly…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.