Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
The set -23 (-0-0-0-0) 16 3 = is a basis for R Use the Gram-Schmict process to produce an orthogonal basis for 111 = V₁ = U₂ = V₂ your answer.) 11 VJ -15 11₁ = V₁ 11 V₂ 111111 To make computations nice, if necessary, we can scale this vector by a non-zero scalar, so that y= ů₁ = us -U₁= uvj V Hi 14 all To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that U₂ = |u₂|| ₂ Va 1₂ U₂ (Do not scale your answer 11₁ u₂V₁ 11₂ 1₁ U₂ = 3 (Do not scale t U₂ Va 11₂ 11₂ To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that Therefore, [u, uz, us. ua) is en orthogonal basis for R. To obtain an orthorormal basis, we scale each of these vectors as follows: -u₂ = (Do not scale your answer) Û₂ = u;= 113 VI 113 113 1 |u₂|| -1₂ = -1₂ = || 13- -6 -6 15

The set -23 (-0-0-0-0) 16 3 = is a basis for R Use the Gram-Schmict process to produce an orthogonal basis for 111 = V₁ = U₂ = V₂ your answer.) 11 VJ -15 11₁ = V₁ 11 V₂ 111111 To make computations nice, if necessary, we can scale this vector by a non-zero scalar, so that y= ů₁ = us -U₁= uvj V Hi 14 all To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that U₂ = |u₂|| ₂ Va 1₂ U₂ (Do not scale your answer 11₁ u₂V₁ 11₂ 1₁ U₂ = 3 (Do not scale t U₂ Va 11₂ 11₂ To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that Therefore, [u, uz, us. ua) is en orthogonal basis for R. To obtain an orthorormal basis, we scale each of these vectors as follows: -u₂ = (Do not scale your answer) Û₂ = u;= 113 VI 113 113 1 |u₂|| -1₂ = -1₂ = || 13- -6 -6 15

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
See similar textbooks
icon
Related questions
Question
The set -23 (-0-0-0-0) 16 is a basis for R Use the Gram-Schmict process to produce an orthogonal basis for ¹. 111 = V₁ = U₂ = V₂ 11 VJ -15 -3 your answer" 11₁ = V₁ U₂ V₂. 11111 To make computations nice, if necessary, we can scale this vector by a non-zero scalar, so that y= ū₁ = us -U₁= 11V₂ HH 11₁ all To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that u₂ = ₂ Va 1₂ U₂ u₂ V4. u₁u₂ 1₁ (Do not scale your answer -= -u₂ = 11₂ 11 (Do not scale r (Do not scale your answer) To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that Therefore, [u, uz, us. u) is en orthogonal basis for R. To obtain an orthorormal basis, we scale each of these vectors as follows: Û₂ = u;= 3 1 113 VI 113 113 -1₂ = |u₁|| -1₂ = Note: To enter a number of the form type a/sqrt(n) Thus, (₁, ₂, 3, 4) is an orthonormal. basis for R 113= -6 -6 -15
Transcribed Image Text:The set -23 (-0-0-0-0) 16 is a basis for R Use the Gram-Schmict process to produce an orthogonal basis for ¹. 111 = V₁ = U₂ = V₂ 11 VJ -15 -3 your answer" 11₁ = V₁ U₂ V₂. 11111 To make computations nice, if necessary, we can scale this vector by a non-zero scalar, so that y= ū₁ = us -U₁= 11V₂ HH 11₁ all To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that u₂ = ₂ Va 1₂ U₂ u₂ V4. u₁u₂ 1₁ (Do not scale your answer -= -u₂ = 11₂ 11 (Do not scale r (Do not scale your answer) To make computations nicer, if necessary, we can scale this vector by a non-zero scalar, so that Therefore, [u, uz, us. u) is en orthogonal basis for R. To obtain an orthorormal basis, we scale each of these vectors as follows: Û₂ = u;= 3 1 113 VI 113 113 -1₂ = |u₁|| -1₂ = Note: To enter a number of the form type a/sqrt(n) Thus, (₁, ₂, 3, 4) is an orthonormal. basis for R 113= -6 -6 -15
Expert Solution
steps

Step by step

Solved in 4 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS