Consider the subspace S of the Euclidean inner product space R4 spanned by the vectors v₁ = (1,1,1,1), v₂= (1,1,2,4), v₂=(1,2,-4,-3). Find an orthogonal basis of S. O A {(1,1,1,1),(1,1,2,4), (1,2,-4,-3)} B{(1,1,2,4),(-1,-1.0.2) (₁.-3.1)} OC. {(2,-3,1),(1,2,-4,-3), (4,2,1,1)} OD. None in the given list. OE. {(1,1,1,1),(-1,-1,0,2), (1,3, -6,2)}
Consider the subspace S of the Euclidean inner product space R4 spanned by the vectors v₁ = (1,1,1,1), v₂= (1,1,2,4), v₂=(1,2,-4,-3). Find an orthogonal basis of S. O A {(1,1,1,1),(1,1,2,4), (1,2,-4,-3)} B{(1,1,2,4),(-1,-1.0.2) (₁.-3.1)} OC. {(2,-3,1),(1,2,-4,-3), (4,2,1,1)} OD. None in the given list. OE. {(1,1,1,1),(-1,-1,0,2), (1,3, -6,2)}
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 given subspace of the Euclidean inner product space spanned by the vectors ,
(.) Othogonal basis : A basis of a subspace of of an inner product space is said to be orthogonal basis if , i.e inner product of every two distinct vectors of S is zero .
where denotes an inner product of the vectors and .
(.) Inner product : Inner product of two vectors and is given by ,
(.) A subspace has infinitely many basis . And every basis has same number of vectors .
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