6C Illustration is given f: R³ R³: (x, y, z)→f(x, y, z) = (x-2y, y-2z, -x+4=) Find the basis change matrix, from the basis B={(-1,1,1), (1,-1,1), (1,1,-1)} to the natural basis of R³ and then find the matrix representation of f with respect to B. Is there a basis of R³ with respect to which the representation matrix of f is inverted?

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A: Solution is below.

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A: Solution by using Gram Schmidt process as follows :

Q: Suppose A is the matrix for T: R³ R³ relative to the standard basis. Find the diagonal matrix A' for…

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Q: Suppose A is the matrix for T: R³ R³ relative to the standard basis. Find the diagonal matrix A' for…

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Q: Suppose A is the matrix for T: R³ → R³ relative to the standard basis. Find the diagonal matrix A'…

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Q: Suppose A is the matrix for T: R³ → R³ relative to the standard basis. Find the diagonal matrix A'…

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