Consider the set of vectors {u" ,v ,w° } in R°, where u =(4,-4,8), v =(9,6,3) and w =(-9,-21,k), with kER. The value of k such that {u",v" ,w }is a linearly dependent set, corresponds to:

Q: Find the vector z, given that u = ⟨1, 2, 3⟩, v = ⟨2, 2, −1⟩, and w = ⟨4, 0, −4⟩     (1/3)z − 3u = w

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A: The detailed solution is as follows below:

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A: Given: Let us consider the given values as ,  A→,B→,C→A→=2a^x+4a^yB→=3a^x+a^zC→=2a^y+3a^z

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Q: Show that v, = v 2 V2 3 span R and express the vector v= as a linear -7 %3D combination of v,,v2.

A: Solve the following

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Q: Let y = 18 || = and u = 6 Write y as the sum of two orthogonal vectors, ₁ in Span {u} and ₂…

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A: Then   -------------(1) Also  --------------------(2)

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( 5 , −…

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Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

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A: Suppose that u,v and w are vectors such thatu,v=2,v,w=-3,u,w=5,u=1,v=2 and w=7Find the value of…

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A: find the explanation below

Q: Find the vector z, given that u = ⟨1, 2, 3⟩, v = ⟨2, 2, −1⟩, and w = ⟨4, 0, −4⟩.      z = u − v + w

A: Given:                                                          u = <1, 2,…

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A: Since you have posted multiple questions, we answered the first question for you. If you want us to…

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Q: Find two vectors v and w such that the projection of v onto w is v.

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Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = ( –…

A: Topic = Vector