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The set is a basis for R*. Use the Gram-Schmidt process to produce an orthogonal basis for R¹ U₁ = V₁ = U₂ = V₂- HOBHA U₁V₂ u₁u₁ U₂ = Vy - scalar, so that u -U₁ To make computations nicer, if necessary, we can scale this vector by a non-zero Up V3 u₁u₁ 0₂-0₂ (Do not scale your answer.) To make computations nicer if necessa (Do not scale your answer.) scale this vector by a non-zero

The set is a basis for R*. Use the Gram-Schmidt process to produce an orthogonal basis for R¹ U₁ = V₁ = U₂ = V₂- HOBHA U₁V₂ u₁u₁ U₂ = Vy - scalar, so that u -U₁ To make computations nicer, if necessary, we can scale this vector by a non-zero Up V3 u₁u₁ 0₂-0₂ (Do not scale your answer.) To make computations nicer if necessa (Do not scale your answer.) scale this vector by a non-zero

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The set U₁ = V₁ = is a basis for R*. Use the Gram-Schmidt process to produce an orthogonal basis for R U₂ = V₂ - HHHHO U₂ = Vy - U₁V₂ u₁u₁ -U₁ To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that u U₁ V3 U₁+U₁ <-17 scalar, so that u U₂ V3 0₂-0₂ (Do not scale your answer.) (Do not scale your answer.) To make computations nicer, if necessary, we can scale this vector by a non-zero
Transcribed Image Text:The set U₁ = V₁ = is a basis for R*. Use the Gram-Schmidt process to produce an orthogonal basis for R U₂ = V₂ - HHHHO U₂ = Vy - U₁V₂ u₁u₁ -U₁ To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that u U₁ V3 U₁+U₁ <-17 scalar, so that u U₂ V3 0₂-0₂ (Do not scale your answer.) (Do not scale your answer.) To make computations nicer, if necessary, we can scale this vector by a non-zero
U₂ = V4- your answer.) û₁ 5 U₁V4 -U₁ U₁U₁ = To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that u 1 ||u₁|| Therefore, (u₁. U₂. u. ₁) is an orthogonal basis for R¹. To obtain an orthonormal basis, we scale each of these vectors as follows: U₂ V4 U₂ U₂ -U₁ = Check U₂ -U = U₂ - V4 U₂ · U₂ 3 u₂ Note: To enter a number of the form type a/sqrt(n). Thus, (û₁. ₂. 3. 4) is an orthonormal basis for R¹ (Do not scale -U₂
Transcribed Image Text:U₂ = V4- your answer.) û₁ 5 U₁V4 -U₁ U₁U₁ = To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that u 1 ||u₁|| Therefore, (u₁. U₂. u. ₁) is an orthogonal basis for R¹. To obtain an orthonormal basis, we scale each of these vectors as follows: U₂ V4 U₂ U₂ -U₁ = Check U₂ -U = U₂ - V4 U₂ · U₂ 3 u₂ Note: To enter a number of the form type a/sqrt(n). Thus, (û₁. ₂. 3. 4) is an orthonormal basis for R¹ (Do not scale -U₂
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