Consider the plane, X, in Rº given by the vector equation: x(s, t) = (1,-1, 2) + s(1,0,1)+t(1,-1,0); = st ER. a) Compute

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Consider The Plane X In Ro Given By The Vector Equation X S T 1 1 2 S 1 0 1 T 1 1 0 St Er A Compute 1 (64.78 KiB) Viewed 17 times

Consider the plane, X, in Rº given by the vector equation: x(s, t) = (1,-1, 2) + s(1,0,1)+t(1,-1,0); = st ER. a) Compute a unit normal vector, n, to this plane. b) Define a linear transformation P: R3 → R3 by projection onto n: P(x):= projn(x), XER3. Compute the standard matrix, A, of P. c) Let B= 13 – A. If Q=TB is the matrix transformation defined by = = 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 € R33 is the standard matrix of P, show that A2 = A. Why is this true?