let v1 12 3 1 v2 0 0 1 2 a 4x1 matrices a let s spanv1v2 ie the subspace generated by v1 and v2

Name: let v1 12 3 1 v2 0 0 1 2 a 4x1 matrices a let s spanv1v2 ie the subspace generated by v1 and v2 construct an orthonormal basis for s b let w be the set of all vectors that are orthogonal to 25192
Uploaded: 2022-12-11T10:15:35-08:00
Duration: 3 min 20 s
Channel: Sri K
Description: let v1 12 3 1 v2 0 0 1 2 a 4x1 matrices a let s spanv1v2 ie the subspace generated by v1 and v2 construct an orthonormal basis for s b let w be the set of all vectors that are orthogonal to 25192

Question

Let v1 = (1 2 3), v2 = (0 0 1 2), as 4x1 matrices. (a) Let S = span{v1,v2}, i.e., the subspace generated by v1 and v2. Construct an orthonormal basis for S. (b) Let W be the set of all vectors that are orthogonal to both v1 and v2, i.e., W = S⊥. Find a basis for W. (c) Show that w = (1 1 1 1), a 4x1 matrix, does not lie in S. Show that w does not lie in W either. Explain why this is possible.

          Let v1 = (1 2 3), v2 = (0 0 1 2), as 4x1 matrices.

(a) Let S = span{v1,v2}, i.e., the subspace generated by v1 and v2. Construct an orthonormal basis for S. 
(b) Let W be the set of all vectors that are orthogonal to both v1 and v2, i.e., W = S⊥. Find a basis for W. 
(c) Show that w = (1 1 1 1), a 4x1 matrix, does not lie in S. Show that w does not lie in W either. Explain why this is possible.

Added by Daniel V.

Calculus: Early Transcendentals

James Stewart 8th Edition

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Solved by Expert Sri K

12/11/2022

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Let v1 = (1 2 3), v2 = (0 0 1 2), as 4x1 matrices. (a) Let S = span{v1,v2}, i.e., the subspace generated by v1 and v2. Construct an orthonormal basis for S. (b) Let W be the set of all vectors that are orthogonal to both v1 and v2, i.e., W = S⊥. Find a basis for W. (c) Show that w = (1 1 1 1), a 4x1 matrix, does not lie in S. Show that w does not lie in W either. Explain why this is possible.