Consider the plane, X, in R3 given by the vector equation: x(s, t) = (1, –1, 2) + s(1, 0, 1) + t(1, –1, 0); s, t E R. %3D a) Compute a unit normal vector, n, to this plane. b) Define a linear...

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Extracted text: Consider the plane, X, in R3 given by the vector equation: x(s, t) = (1, –1, 2) + s(1, 0, 1) + t(1, –1, 0); s, t E R. %3D a) Compute a unit normal vector, n, to this plane. b) Define a linear transformation P : R' → R' by projection onto n: P(x) := proj, (x), xE R'. Compute the standard matrix, A, of P. c) Let B = I3 – A. If Q = TB is the matrix transformation defined by %3D Q(x) = Bx, show that Q is the projection onto the plane, X. That is, show that Q(x) = x if x is parallel to X and that Q(x) = 0 if x is orthogonal (normal) to X. d) If A E RX3 is the standard matrix of P, show that A = A. Why is this true? 2