Let u = (a11, a12, a13), v = (a21, a22, a23), w = (a31, a32, a33) be three vectors in R³. Explain, using linear algebra, why it is (generally) impossible to find a nonzero vector (x, y, z) that is orthogonal to u, v and w. Your explanation should refer to the properties of a relevant system of linear equations.

Let u = (a11, a12, a13), v = (a21, a22, a23), w = (a31, a32, a33) be three vectors in R³. Explain, using linear algebra, why it is (generally) impossible to find a nonzero vector (x, y, z) that is orthogonal to u, v and w. Your explanation should refer to the properties of a relevant system of linear equations.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 74E: Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors...

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