We have three vectors ủ, v and w in R4: 1 2 1 -1 1 (7a) Are these vectors ū, v and ú linearly independent? Justify your answer. (7b) Find a vector x E Rª that is not in the span of ủ, v and w. Make sure to provide an explanation of why x is not in the span of ū, v and w.

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A: As per our guidelines, we are allowed to answer only question. Since, you have posted multiple…

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A: follow next step

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A: Orthonormal vectors are perpendicular to each other.

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A: Find your answer below

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A: The unit vector,  , in the direction of the vector is calculated as follows.

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A: The detailed solution is given below Thank you

Q: The vectors w = x= y = and z = are linearly independent. O linearly dependent. If the vectors are…

A: The solution is follows:

Q: Verify that the two planes are parallel. -x + 6y + 2z = 7 %3! +3y +z 8 Find the normal vector, n,,…

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A: Given that u and v are two nonzero vectors   Dot product of two nonzero vectors u.v=|u|.|v|…

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Q: b) Find out the Vector =y²z?i+x?z?j+z²y²k is irrotational or not?

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Q: 1. Show that the vectors u̟ and uz parallel to lines L1 and L2 respectively, are orthogonal. L1: x =…

A: The given equations of lines are: L1:x=5-2t, y=-7+t, z=6+4t and L2:x=2+3t, y=5+2t, z=1+t Rewriting…

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A: Given: u=4,-5z=-11,-10