(3, 2, 1), (8, (a) Prove, by direct calculation, that S is an orthogonal subset of R³. b) Prove that S is a basis for R³. (c) Use Theorem 6.3 to write (–1,1, –1) as a lincar combination of the vectors in S. Theorem 6.3. Let V be an inner product space and S = {v1,v2, … ..,Uk} be an orthogonal subset of V consisting of nonzero vectors. If y E span (S), then - (y, v;). Lshi

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Hello, I need help with this Linear Algebra exercise, please. Thank you!

Let S = {(2, 1, –2), (3, 2, 4), (8, –14, 1)}.
(a) Prove, by direct calculation, that S is an orthogonal subset of R³.
(b) Prove that S is a basis for R³.
(c) Use Theorem 6.3 to write (–1,1, –-1) as a lincar combination of the vectors in S.
Theorem 6.3. Let V be an inner product space and S = {v1, V2, . .., Uz} be an orthogonal subset of V
consisting of nonzero vectors. If y E span (S), then
(y, v;)
y =
we proved this in Example 1
i=1
Transcribed Image Text:Let S = {(2, 1, –2), (3, 2, 4), (8, –14, 1)}. (a) Prove, by direct calculation, that S is an orthogonal subset of R³. (b) Prove that S is a basis for R³. (c) Use Theorem 6.3 to write (–1,1, –-1) as a lincar combination of the vectors in S. Theorem 6.3. Let V be an inner product space and S = {v1, V2, . .., Uz} be an orthogonal subset of V consisting of nonzero vectors. If y E span (S), then (y, v;) y = we proved this in Example 1 i=1
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