Consider the vector v = (1, 6, -1) in R. Let W be the subspace of R consisting of all vectors of the form (a, b, a - 2b). Decompose v into the sum of a vector that lies in W, w, and a vector orthogonal to W, w. V = w + w =

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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Linear Algebra. Please write your answer clearly.

Consider the vector v = (1, 6, -1) in R. Let W be the subspace of R consisting of all vectors of the form (a, b, a – 2b). Decompose v into the sum of a vector that lies in W,
w, and a vector orthogonal to W, w.
V = w + W =
+
Transcribed Image Text:Consider the vector v = (1, 6, -1) in R. Let W be the subspace of R consisting of all vectors of the form (a, b, a – 2b). Decompose v into the sum of a vector that lies in W, w, and a vector orthogonal to W, w. V = w + W = +
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