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in vector space R4, consider the internal product defined by (u,v) = ₁v₁ + u₂vq u2v3-U3v3+3u3v3+2u4v4 and the standard associated with it, ie ||v|| = √ (v,v). Remember that a vector is called unitary if its norm is equal to one. In relation to this internal product, answer the following items, mathematically justifying your statements. 1- Determine the value of the scalar K so that the vectors u = (0.5,K,0) and v= (0,0,1,0) are orthogonal. 2- Let W be the vector subspace of R* formed by the vectors that have the first and fourth null components. Obtain a basis of W where the vectors are orthogonal and unitary.

in vector space R4, consider the internal product defined by (u,v) = ₁v₁ + u₂vq u2v3-U3v3+3u3v3+2u4v4 and the standard associated with it, ie ||v|| = √ (v,v). Remember that a vector is called unitary if its norm is equal to one. In relation to this internal product, answer the following items, mathematically justifying your statements. 1- Determine the value of the scalar K so that the vectors u = (0.5,K,0) and v= (0,0,1,0) are orthogonal. 2- Let W be the vector subspace of R* formed by the vectors that have the first and fourth null components. Obtain a basis of W where the vectors are orthogonal and unitary.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.3: Lines And Planes
Problem 47EQ
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4 in vector space R*, consider the internal product defined by (4,v) = 41V1+ u2v2 – ugV3 – UzV3+ 3u3v3+ 2u4°4 and the standard associated with it, ie |v|| = v (v,v). Remember that a vector is called unitary if its norm is equal to one. In relation to this internal product, answer the following items, mathematically justifying your statements. 1- Determine the value of the scalar K so that the vectors (0.5, K,0) and v = (0,0,1,0) are orthogonal. 2 - Let W be the vector subspace of R* formned by the vectors that have the first and fourth null components. Obtain a basis of W where the vectors are orthogonal and unitary. u = 4
Transcribed Image Text:4 in vector space R*, consider the internal product defined by (4,v) = 41V1+ u2v2 – ugV3 – UzV3+ 3u3v3+ 2u4°4 and the standard associated with it, ie |v|| = v (v,v). Remember that a vector is called unitary if its norm is equal to one. In relation to this internal product, answer the following items, mathematically justifying your statements. 1- Determine the value of the scalar K so that the vectors (0.5, K,0) and v = (0,0,1,0) are orthogonal. 2 - Let W be the vector subspace of R* formned by the vectors that have the first and fourth null components. Obtain a basis of W where the vectors are orthogonal and unitary. u = 4
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