Do the given vectors form an orthogonal basis for R³?--0-4=V₂V3V1are given by[w] BYes, the given set does form an orthogonal basis for R³.O No, the given set does not form an orthogonal basis for R³.=You are given the theorem below.Let {V₁, V₂, ..., V} be an orthogonal basis for a subspace W of Rn and let w be any vector in W. Then the unique scalars c₁₁W = C₁V₁ + ... + CkvkC₁1W = 10-11-1W. VV¡ . ViUse the theorem to express w as a linear combination of the above basis vectors. Give the coordinate vector [w] of w with respect to the basis B = {V₁, V₂, V3} of R³.B11for i = 1, ..., k.C such that

The given vectors are v1=10-1,v2=121,v3=1-11. We have to find the Linear combination for w=111.

Do the given vectors form an orthogonal basis for R³? V₁ = Yes, the given set does form an orthogonal basis for R³. O No, the given set does not form an orthogonal basis for R³. You are given the theorem below. Let {V₁, V2¹ 1 0 V₂ = 2 V3 = -1 are given by [W] B ..., vbe an orthogonal basis for a subspace W of R and let w be any vector in W. Then the unique scalars c₁, W = C₁V₁ + + CkV k w.Vi for i = 1,..., k. V;. Vi Use the theorem to express w as a linear combination of the above basis vectors. Give the coordinate vector [w] of w with respect to the basis B = {V₁, V₂, V3} of R³. C₁ = W = 1 ... C such that 000

Do the given vectors form an orthogonal basis for R³? V₁ = Yes, the given set does form an orthogonal basis for R³. O No, the given set does not form an orthogonal basis for R³. You are given the theorem below. Let {V₁, V2¹ 1 0 V₂ = 2 V3 = -1 are given by [W] B ..., vbe an orthogonal basis for a subspace W of R and let w be any vector in W. Then the unique scalars c₁, W = C₁V₁ + + CkV k w.Vi for i = 1,..., k. V;. Vi Use the theorem to express w as a linear combination of the above basis vectors. Give the coordinate vector [w] of w with respect to the basis B = {V₁, V₂, V3} of R³. C₁ = W = 1 ... C such that 000

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

Do the given vectors form an orthogonal basis for R³?
--0-4
=
V₂
V3
V1
are given by
[w] B
Yes, the given set does form an orthogonal basis for R³.
O No, the given set does not form an orthogonal basis for R³.
=
You are given the theorem below.
Let {V₁, V₂, ..., V} be an orthogonal basis for a subspace W of Rn and let w be any vector in W. Then the unique scalars c₁₁
W = C₁V₁ + ... + Ckvk
C₁
1
W = 1
0
-1
1
-1
W. V
V¡ . Vi
Use the theorem to express w as a linear combination of the above basis vectors. Give the coordinate vector [w] of w with respect to the basis B = {V₁, V₂, V3} of R³.
B
1
1
for i = 1, ..., k.
C such that

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