show that the vectors V₁ = (2,0,- 2, 1) > V₂ = (3,1, -5,0) and V3=(2, 2, -6, -2) form Linearly defendent set in R4 and express each vector as a linear Combination of others

Q: define (2a - b + 4c, 3a-c, 4b + c) as a linear combination of three nonzero vectors

A: We have to define  (2a - b + 4c, 3a - c, 4b + c) as a linear combination of three nonzero vectors

Q: If x is an n-vector, show that x + 0 = x.

A: Given, If x is an n-vector.

Q: Show whether or not the set of vectors B = {U, V, W} where U = V = and W = 0 is a basis for R³.

A:

Q: Find the vector P,P2 and P2P1 P:(3.2,3) , Р.(5,7,-1) b- P1(-2,-1,0), P2(4,-5,2) a - P1(0,3,3),…

A: We can solve the given problem as follows:

Q: Let a = (2,3,6) and b = (3,4,2) be vectors.  Compute the cross product aXb

A:

Q: Find the length of the vector x=x= |x|=|x|=

A:

Q: Show that the column vectors (1,1,2,4), (2,-1,-5,2), (1,-1,-4,0) and (2,1,1,6) vectors in R are…

A:

Q: Add the vectors E = , F=, G .

A:

Q: Determine whether the given vectors (1, 1,-1, 1), (1,-1, 2,-1), (3, 1, 0, 1) in R* are lincarly…

A: Given vectors are: (1, 1, -1, 1) , (1, -1, 2, -1) , (3, 1, 0, 1) We have to determine whether the…

Q: Which of the following sets of vectors are linearly dependent? (i) {(2,3), (-4,-6)}; (ii) ((0, 4,0,…

A:

Q: Construct a vector that is perpendicular to the plane containing (−2, 4, 1),(3, 3, -1) and (1, 0,…

A: Construct a vector that is perpendicular to the plane containing (-2,4,1),(3,3,-1) and (1,0,2)

Q: Express the vector p = (-6,15,-3) as linear combination of the vectors u = (1,-1,3), v = (2,-5,0)…

A:

Q: 5) Find a vector in component form that is orthogonal to the vectors a = (9,3,-7) and b = (10,-8,2)

A:

Q: Find a maximal set of linearly independent vectors out of the set {v1 = (1,2, 3, 4), v2 = (2, 3, 4,…

A: From given set of vectors we have to find maximal set of linearly independent factors. Concept: Let…

Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: Show that the column vectors (1,1.2,4), (2,-1,-5,2). (1,-1,-4,0and (2,1,1.6) vectors in R are…

A: We have to prove that the given Column vectors are linearly dependent in R4.

Q: If possible express the vector v as a linear combination of V1, V2, and V3. (b) v = (0, 0, -1), V₁ =…

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Q: Show that the column vectors (1,1,2,4), (2,-1.-5.2), (1.-1,-4,0) and (2,1.1,6) vectors in R are…

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Q: Let V₁, V2, V3 be the vectors in R³ defined by 18 ---A V2 = -14 (a) Is (V1, V₂, V3} linearly…

A: We now solve this questions

Q: Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.)…

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Q: Let the following vectors be in R³ a = (1,3,-1) b = (-2,1,3) c = (3,2,1) d= (1,-1,2) 14.- Perform…

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Q: Prove that swapping the order of vectors in the cross product changes the sign of the output: ьха3 -…

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