Let B, D be the following two bases of R³: B = D= 0 0 -2 2 a) Find the change of coordinates matrix PDB from the basis B to D. 2 0 -2 }]}

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A: The detailed solution is as follows below:

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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: Solution is below.

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A: Let U={u1,u2,⋯,un} and V={v1,v2,⋯,vn} are two bases of a vector space W.The identity map I:W→W…

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Q: 4 [1] 2. Is the vector 5 in the column space of matrix A = 1 0 -2 −4 4 4 5 3 -13]

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A: 1) Let Tabcd=0a+0b+0c+4d1a+(-1)b+(-2)c+4d0a+1b+(-2)c+5d1a+(-1)b+(-2)c+2d2a+1b+(-10)c+4d   To Find:…