Suppose S = {r, u, d} is a set of linearly independent vectors. If x = 2r+u+ 5d, determine whether T = {r, u, x} is a linearly independent set. 1. Is T linearly independent or dependent? Select an Answer If T' is dependent, enter a non-trivial linear relation below. Otherwise, enter O's for the coefficients. Or+u+x=0.

Q: Let u = (3, 5, -7) and v = (6, -5, 1). Evaluate u + v and 3u - v.

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Q: Let u4 be a linear combination of {u₁, U₂, U3}. Select the best statement. OA. {U₁, U₂, U3, U4}…

A: Given that, be a linear combination of .The aim is to find the correct statement about the given…

Q: Show that V1, V2, V3 are linearly independent, but V₁, V2, V3, V4 are not. Then express V4 as a…

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Q: Describe geometrically (line, plane, or all of R 3) all linear combinations of (a) [ 1/2/3 ] and […

A: We know that a set of vectors u1, u2, ……, un is said to be linearly independent if the equation…

Q: Select the best statement.

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Q: (c) Determine whether the set R², with the operations (x₁, y₁) + (x₂, y/₂) = (x,,0) and c(x, y) =…

A: Let V be the vector space if  1 If u,v∈V  then u+v ∈V 2.  u+v=v+u 3. (u+v)+w=u+(v+w) 4. Identity…

Q: Let u = (5,-5, -7) and 7 = (-6, 1, 2). Compute the following: úxv= v X ū= úxu 3 (u xv) = ū × (30) =…

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Q: Let i = (– 3, - 2, 3) and i = (1, – 6, – 7). Compute the following: i xü = i x ủ u X u =

A: Since you have asked a question with multiple parts in a single request, we would be answering only…

Q: 3. Check whether (2, 4) and (1, 2) are linearly dependent or not?

A: Linearly department vectors

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

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Q: Let a = (2, – 3, – 1) and b = (– 5, – 1, k). %3D %3D - Find k so that a and b will be orthogonal.…

A: Since we have been given that a⇀ = <2, -3, -1> and b⇀ = <-5, -1, k>Our aim is to find…

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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: 1 1 Let A = Find the values of a such that A is not diagonalizable 1 1 0 0 1

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Q: Suppose v4 = 20 – 02 + 503. Let w = 601 + 202 – 303 – 204. (a) Write w as a linear combination of…

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Q: Question 2: For which real values of a do the polynomials P1(t) = at? -t-; P2(t) = - + at -; P3(t) =…

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Q: Let u = = (–3, 3, 5) and v = (−6, −4, −7). Compute the following: ū X x v = v × x ū x ū ū=

A: Please note that as per bartleby guidelines, we need to answer only the first three sub-parts.Kindly…

Q: Let a = (1, – 5, 3) and b = ( – 5, 3, k). | Find k so that a and b will be orthogonal. k =

A: a→=1,-5,3b→=-5,3,k To find: value of k for which both will be orthogonal.

Q: Consider the linear operator T: R? → R² defined by the following equations. w1 = 3x1 + 11x, W2 = X1…

A: we have to find the inverse of T          (i.eT-1(w1,w2))where T:R2→R2 is given by…

Q: Find w such that 2u + v – 3w = 0. u = (2, 7, 5, 0), v = (-3, 1, W =

A: Addition and subtraction of two vectors: Add or subtract the necessary components to add or subtract…

Q: 3. Find all real numbers t for V = (20 t,4t - 4,5t², t²) are orthogonal. - which = (1,5t,-4t, t³)…

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Q: 1 5 ]v s or fractions.) W = - 3 0

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Q: Please explain properties or rules for each step

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Q: Let u = (−3,2,1,0), v = (4,7,−3,2), and w = (5, −2, 8, 1). Find the components of −u+(v−4w)

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Q: If u = [3, - 1] and v = [1,4],compute and draw u + v.

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Q: Let = [-5 1] and = [6-6]. Find the following vectors. [ = -6y = [ w = 5x – 6y = [ | v=5z ]]

A: A detailed solution is given below.

Q: v1 =[ 2 5 1 ] , v2 =[ − 3 1 − 1 ] , b =[ 11 19 5 ] Show that b is in Span{v1,v2}. Express b as a…

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

A: We have to find