10. Let (1,2,3) be a solution for the vector equation ru + yv + zw = 0 and consider the matrix A=[u,v,w] representing a linear transformation T. Pick the best option: a) NullSpace(T)={0} b) Range(T)={0} c) The list (u,v,w) is a basis for Nullspace(T) d) Dimension(Range(T)) < 3.

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A: We will find out the required solution.

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Q: Show linear dependence in part (ii) to show that ({1,0,1}) is a basis.

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A: The solution are next step

Q: The matrix that projects onto the x-y plane is

A: We have to find the matrix that project onto  plane

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A: The given vectors  and .The objective is to find the orthogonal complement of the given vectors.

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A: Recall:A set of vectors is said to be linearly dependent if the determinant is zero.If the…

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Q: Consider the vectors ā₁ = (-1,2,2), a2 = (2,2, -1), and 3 = (2,-1,2). 1. Compute the projection…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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