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Show that (u₁, U₂, U3) is an orthogonal basis for R³. Then express x as a linear combination of the u's. U₁ = 5 -5 4₂5 2 2 -1 U3 = **** OA. U₁-25 ₂ = u₁-u3 = 4₂-43 = 1 1 4 + Which of the following criteria are necessary for a set of vectors to be an orthogonal basis for a subspace W of R? Select all that apply. and x = A. The vectors must span W. B. The vectors must form an orthogonal set. C. The vectors must all have a length of 1. D. The distance between any pair of distinct vectors must be constant. Which theorem could help prove one of these criteria from another? OA. IfS={U₁. up) and each u, has length 1, then S is an orthogonal set and hence is a basis for the subspace spanned by S. OB. If S= (u₁... up) and the distance between any pair of distinct vectors is constant, then the vectors are evenly spaced and hence form an orthogonal set.. OC. If S= (₁. Up}! is a basis in RP, then the members of S span RP and hence form an orthogonal set. OD. If S = (u₁.... up) is an orthogonal set of nonzero vectors in R", then S is linearly independent and hence is a basis for the subspace spanned by S. Which calculations should be performed next? (Simplify your answers.) Vis 5 -2 How do these calculations show that (u₁, U₂, U3} is an orthogonal basis for R³? Since each the vectors Express x as a linear combination of the u's. x= (Use integers or fractions for any numbers in the equation.) OB. From the theorem above, this proves that the vectors are also 4₁4₂ UU U₂U3 =

Show that (u₁, U₂, U3) is an orthogonal basis for R³. Then express x as a linear combination of the u's. U₁ = 5 -5 4₂5 2 2 -1 U3 = **** OA. U₁-25 ₂ = u₁-u3 = 4₂-43 = 1 1 4 + Which of the following criteria are necessary for a set of vectors to be an orthogonal basis for a subspace W of R? Select all that apply. and x = A. The vectors must span W. B. The vectors must form an orthogonal set. C. The vectors must all have a length of 1. D. The distance between any pair of distinct vectors must be constant. Which theorem could help prove one of these criteria from another? OA. IfS={U₁. up) and each u, has length 1, then S is an orthogonal set and hence is a basis for the subspace spanned by S. OB. If S= (u₁... up) and the distance between any pair of distinct vectors is constant, then the vectors are evenly spaced and hence form an orthogonal set.. OC. If S= (₁. Up}! is a basis in RP, then the members of S span RP and hence form an orthogonal set. OD. If S = (u₁.... up) is an orthogonal set of nonzero vectors in R", then S is linearly independent and hence is a basis for the subspace spanned by S. Which calculations should be performed next? (Simplify your answers.) Vis 5 -2 How do these calculations show that (u₁, U₂, U3} is an orthogonal basis for R³? Since each the vectors Express x as a linear combination of the u's. x= (Use integers or fractions for any numbers in the equation.) OB. From the theorem above, this proves that the vectors are also 4₁4₂ UU U₂U3 =

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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Show that (u₁, U₂, U3) is an orthogonal basis for R³. Then express x as a linear combination of the u's. U₁₁ = 5 -5 U₂ = 0 2 2 -1 B. If S= U3 = + Which of the following criteria are necessary for a set of vectors to be an orthogonal basis for a subspace W of R? Select all that apply. OA. U₁ - U₂ = u₁-u3 = 4₂-43 = 1 A. The vectors must span W. B. The vectors must form an orthogonal set. C. The vectors must all have a length of 1. D. The distance between any pair of distinct vectors must be constant. Which theorem could help prove one of these criteria from another? 4 OA. If S= (u₁.... up) and each u, has length 1, then S is an orthogonal set and hence is a basis for the subspace spanned by S. Since each 5 and x = -2 = {4₁, ..... up and the distance between any pair of distinct vectors is constant, then the vectors are evenly spaced and hence form an orthogonal set. up is a basis in RP, then the members of S span RP and hence form an orthogonal set. OC. If S= {u₁ OD. If S = {u,₁,...,up) is an orthogonal set of nonzero vectors in R", then S is linearly independent and hence is a basis for the subspace spanned by S. Which calculations should be performed next? (Simplify your answers.) is How do these calculations show that {u₁, U2, U3} is an orthogonal basis for R³? the vectors Express x as a linear combination of the u's. x=₁+₂+3 (Use integers or fractions for any numbers in the equation.) OB. From the theorem above, this proves that the vectors are also ₁4₂= 13 4₂ 43 =
Transcribed Image Text:Show that (u₁, U₂, U3) is an orthogonal basis for R³. Then express x as a linear combination of the u's. U₁₁ = 5 -5 U₂ = 0 2 2 -1 B. If S= U3 = + Which of the following criteria are necessary for a set of vectors to be an orthogonal basis for a subspace W of R? Select all that apply. OA. U₁ - U₂ = u₁-u3 = 4₂-43 = 1 A. The vectors must span W. B. The vectors must form an orthogonal set. C. The vectors must all have a length of 1. D. The distance between any pair of distinct vectors must be constant. Which theorem could help prove one of these criteria from another? 4 OA. If S= (u₁.... up) and each u, has length 1, then S is an orthogonal set and hence is a basis for the subspace spanned by S. Since each 5 and x = -2 = {4₁, ..... up and the distance between any pair of distinct vectors is constant, then the vectors are evenly spaced and hence form an orthogonal set. up is a basis in RP, then the members of S span RP and hence form an orthogonal set. OC. If S= {u₁ OD. If S = {u,₁,...,up) is an orthogonal set of nonzero vectors in R", then S is linearly independent and hence is a basis for the subspace spanned by S. Which calculations should be performed next? (Simplify your answers.) is How do these calculations show that {u₁, U2, U3} is an orthogonal basis for R³? the vectors Express x as a linear combination of the u's. x=₁+₂+3 (Use integers or fractions for any numbers in the equation.) OB. From the theorem above, this proves that the vectors are also ₁4₂= 13 4₂ 43 =
is for the subspace spanned by S. OB. u₁ U₂ = U₁ U₂ = U₂U3= ectors are also OC. u₁u₁" U₂U₂ UzU3
Transcribed Image Text:is for the subspace spanned by S. OB. u₁ U₂ = U₁ U₂ = U₂U3= ectors are also OC. u₁u₁" U₂U₂ UzU3
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