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Q1) Make a matrix A whose columns come from the following set of vectors S: 2 S= 2 a) Find ATA Solution: 6 -1 5 2 -51 3 3 -1 6. 6. A" A = 3 0 9 0 0 2 3 -5 9. b) Now using a) create an orthonormal basis for Span(S). Do NOT use Gram-Schmidt. Hint: aTaj= aj.aj=? a1.a1=6, a2.a2=6, a3.a3=9, a4.a4=9, as.as=9 Three independent vectors are all we need to span all of R3 a3.a4=0, a3.as=0, a4.as=0 => a3, a4, as are orthogonal to each other. Q = { az a4 as llas|l'lla, |l' llas||

Q1) Make a matrix A whose columns come from the following set of vectors S: 2 S= 2 a) Find ATA Solution: 6 -1 5 2 -51 3 3 -1 6. 6. A" A = 3 0 9 0 0 2 3 -5 9. b) Now using a) create an orthonormal basis for Span(S). Do NOT use Gram-Schmidt. Hint: aTaj= aj.aj=? a1.a1=6, a2.a2=6, a3.a3=9, a4.a4=9, as.as=9 Three independent vectors are all we need to span all of R3 a3.a4=0, a3.as=0, a4.as=0 => a3, a4, as are orthogonal to each other. Q = { az a4 as llas|l'lla, |l' llas||

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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Q1) Make a matrix A whose columns come from the following set of vectors S: 2 S= 2 a) Find ATA Solution: 6 -1 5 2 -51 6. 3 3 -1 6. A" A = 3 0 9 0 0 2 3 L-5 9. b) Now using a) create an orthonormal basis for Span(S). Do NOT use Gram-Schmidt. Hint: aTaj= aj.aj=? a1.a1=6, a2.a2=6, a3.a3=9, a4.a4=9, as.as=9 Three independent vectors are all we need to span all of R3 a3.a4=0, a3.as=0, a4.as=0 => a3, a4, as are orthogonal to each other. Q = { az a4 as lla3|l' lla,|l' llas|| 2
Transcribed Image Text:Q1) Make a matrix A whose columns come from the following set of vectors S: 2 S= 2 a) Find ATA Solution: 6 -1 5 2 -51 6. 3 3 -1 6. A" A = 3 0 9 0 0 2 3 L-5 9. b) Now using a) create an orthonormal basis for Span(S). Do NOT use Gram-Schmidt. Hint: aTaj= aj.aj=? a1.a1=6, a2.a2=6, a3.a3=9, a4.a4=9, as.as=9 Three independent vectors are all we need to span all of R3 a3.a4=0, a3.as=0, a4.as=0 => a3, a4, as are orthogonal to each other. Q = { az a4 as lla3|l' lla,|l' llas|| 2
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