Suppose v,, v,,V3 are distinct points on one line in R" . The line need not pass through 29 the origin. Prove that {v,,v2,V3} is a linearly dependent set.

Q: Prove that the three points (;q, yx), (x2, y2), and (x3, y3) are collinear (lie on the same line) if…

A: Given : The three points are : x1, y1, x2, y2 and x3, y3 Now we have to prove that  x1, y1, x2, y2…

Q: Let P1, P2, P3, .. , P78 be some coplanar points with k lines on the same plane. If exactly two line…

A: Given,  P1, P2,P3,...,P78 be some coplanar points with k lines on the same plane. If exactly…

Q: If {x, y} and {z, w} are both linearly independent sets in R^n, then {x, y, z, w} is also linearly…

A: Answer

Q: Show that the list of vectors {r + 2, x² + 2, x³ – 3, x4 – x² + 1} is a linearly independent set of…

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Q: Prove that if ||u|| = ||v||, then u + v and u- v are orthogonal.

A: Given: Let u and v are two vectors. To prove: If ||u||=||v||, then u+v and u-v are orthogonal.…

Q: Determine whether the set {P₁, P2, P3} is linearly independent in P₂=1+2x+3x² + 4x³ and p3 P₂, where…

A: The solution follows as:

Q: Suppose T E L(V, W) and v1, ..., Vm is a list of vectors in V such that Tv1,..., Tvm is a linearly…

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Q: (a) Prove that u + vand u - v are orthogonal in IR" if and only if ||u|| = ||v||. (b) Draw a diagram…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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

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Q: Suppose {u1, Span{u;}nSpan{w;}={0}. Ur, W1, Ws} is a linearly independent subset of V. Show that •..…

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Q: Let u = (2,3, 1), v = (1,3,0), and w = (2,23, 3). Since (1\2)u – (2\3)v – (1\6)w = (0,0,0), can we…

A: No we can't

Q: Prove that (i) the three points A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6) are collinear, (ii) the four…

A: (1) Given points are A(1, 4, 2), B(3, 2, 4) and C(5, 0, 6)

Q: Show that u and v are parallel if and only if u×v = 0.

A: The cross product of two vectors are defined as u×v=uvsinθ. Two vectors are parallel if the angle…

Q: - Show that the vectors X, - () 5e3t and X2 = ) 2et 7et form a linearly independent set.

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Q: {₁,...,} is linearly independent if and only if {₁,...,} is an orthogonal set. True False

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Q: If S = {u, v} is a linearly independent set, then S'= {2u + v, v - u} is linearly independent. O…

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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…

Q: Suppose that the three numbers r1, r2, and r3 are dis- tinct. Show that the three functions…

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Q: 1. Explain why the following form linearly dependent sets of vec- tors. (Solve this problem by…

A: According to our guidelines we can do only one question if multiple question are posted. Please post…

Q: Let v (k,2k,1) and w (k,-1,-8). For which values of k are v andw orthogonal?

A: Calculation:Since it is given that v and w are orthogonal, v ∙ w = 0.

Q: Consider the set S = {p, q, r}, where p=1+x, q= x-x² and r= 1+ 2x². Show that the set S is linearly…

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

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Q: 1. Let a = (1, 1, –1) and b = (2,4, 6). Find the cross product a x b and verify that it orthogonal…

A: Given: a=1, 1, -1b=2, 4, 6 To Find:  To find the cross product a×b, and, to verify that it is…

Q: a) Prove that ||u + v|| = ||u - v|| if and only if u and v are orthogonal, (b) Draw a diagram…

A: a) Suppose u,v are orthogonal. Now…

Q: When V is spanned by {v1, v2, . . . , vk} and one of these vectors can be written as a linear…

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Q: Suppose S = {r,u, d} is a set of linearly independent vectors. If x = 2r + 2u + 2d, determine…

A: Given :  S = {r, u, d} is linearly independent set of vectors  and  x = 2r+2u+2d. To find :  We have…

Q: Let = (1,2). - a. Explain graphically the set S = {(x, y) : (x − 3, y − 1) · ʊ = 0}. b. Draw the the…

A: v→=1,  2 S=(x, y) : x-3, y-1·v→=0

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: Let S{v1,v2, V3}, where -1° 2. ; V1= -1 ; V1 = 1. 1. 1. 5. Show that S is a linearly dependent set,…

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Q: Compute the orthogonal projection of i = onto the line L through and the origin. proj, (1) =

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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: Let u = (1, 2, 3, 4), v = (0, 2, t, 3), and w = (1, 1, 0, 1). Find t so that u + v and w are…

A: Here, u=(1,2,3,4),v=(02,t,3) & w=(1,1,0,1)

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

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Q: Suppose that {u, v} is a linearly independent set. Show that the set {u – v, u + v} is also linearly…

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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: Every orthogonal set in R" is not a linearly dependent set. Select one: True False

A: Statement:   Every orthogonal set in Rn is not a Linearly Dependent set.

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

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Q: Show that the vectors X1 = 2e2t and 2et X2 5e3t form a linearly independent set.

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Q: When the set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2, . . . ,…

A: We have given; The set of vectors {u1, u2, . . . , un} is linearly independent and the set {u1, u2,…

Q: In writing v as a linear combination of u ,,u, &u, ( if possible) given: y = (3,0, – 6) , u,= (1, –…

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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: Let u = (2, 3, 1), v = (1, 3, 0), and w = (2, -3, 3). Since (1/2)u - (2/3)v - (1/6)w = (0, 0, 0),…

A: Given: u = (2, 3, 1), v = (1, 3, 0), and w = (2, -3, 3). And, (1/2)u - (2/3)v - (1/6)w = (0, 0, 0),…

Q: S is a linearly independent set,then for any x element of , x is not the linear combination of other…

A: Since, using the following definition of linearly dependent of sets-If a set of vectors is linearly…

Q: Suppose {u,..., 4,, W1, ..., W,} is a linearly independent subset of V. Show that span (u;)…

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Q: Suppose v1, v2, v3, 04, Üz and v6 are vectors in R6 satisfying the following linear relation: 201 +…

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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…