Show that T(x1, x2, x3) = (3x₁ - 6x3, x2 + x3, x1 - x2 - 2x3) is a linear trans- ormation by finding a matrix that implements the mapping. Note that x1, x2, and x3 re not vectors but are entries in vectors. Determine if the linear transformation from the previous problem is (a) onto b) one-to-one

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A: The given statement is False.

Q: [61] Diagonalize B = (by finding P and D) or explain why B isn't diagonalizable.

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Q: Let X = TONT. 1 and 3 0 A = 0 3 1 0 -2 -4 -4 0 3 00 -2 0 0 -4 0 1 -1 01 1 0 0

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A: Properties of transpose of a matrix: (AB)⊥ = B⊥A⊥ Given: (ABC)⊥.

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A: Given: A matrix A=2-1-1-12-1-1-12 To find:  a matrix P that orthogonally diagonalizes A. B=P-1AP

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