5. Consider the inner product defined on R³ by = (a) Let u₁ (2, 1, 2), 1₂ (4, -1, 1), and u3 = (9, 9, 9), and consider the basis B Apply the Gram-Schmidt algorithm to B to produce a new basis B' orthonormal with respect to the above inner product. (b) Express w = (3, 1, 1) as a linear combination of the vectors in B'. 1 1 (u, v) = U₁v₁+U₂ V2 + U3V3. = = {U₁, U2, U3}. {V1, V2, V3} which is =

Advanced Engineering Mathematics
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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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5. Consider the inner product defined on R³ by
(a) Let u₁
(2,1,2), u₂
(4, -1, 1), and u3 = (9, 9, 9), and consider the basis B
Apply the Gram-Schmidt algorithm to B to produce a new basis B'
orthonormal with respect to the above inner product.
(b) Express w = (3, 1, 1) as a linear combination of the vectors in B'.
=
1
1
(u, v) = U₁v₁+U₂ V2 + U3V3.
=
=
{U₁, U2, U3}.
{V1, V2, V3} which is
=
Transcribed Image Text:5. Consider the inner product defined on R³ by (a) Let u₁ (2,1,2), u₂ (4, -1, 1), and u3 = (9, 9, 9), and consider the basis B Apply the Gram-Schmidt algorithm to B to produce a new basis B' orthonormal with respect to the above inner product. (b) Express w = (3, 1, 1) as a linear combination of the vectors in B'. = 1 1 (u, v) = U₁v₁+U₂ V2 + U3V3. = = {U₁, U2, U3}. {V1, V2, V3} which is =
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