Normalizing an Orthogonal Set In Exercises 13-16, (a) show that the set of
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Elementary Linear Algebra (MindTap Course List)
- Showing Linear Dependence In Exercises 53-56, show that the set is linearly dependent by finding a nontrivial linear combination vectors in the set whose sum is the zero vector. Then express one of the vectors in the set as a linear combinations of the other vectors in the set. S={(1,2,3,4),(1,0,1,2),(1,4,5,6)}arrow_forwardTrue or False? In Exercises 55 and 56, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. a A set S of vectors in an inner product space V is orthonormal when every vector is a unit vector and each pair of vectors is orthogonal. b If a set of nonzero vectors S in an inner product space V is orthogonal, then S is linearly independent.arrow_forwardProofIn Exercises 65and 66, prove that the set of vectors is linearly independent and spans R3. B={(1,2,3),(3,2,1),(0,0,1)}arrow_forward
- Testing for a Vector SpaceIn Exercises 13-36, determine whether the set, together with the standard operations, is a vector space. If it is not, identify at least one of the ten vector space axioms that fails. The set of all 22 singular matricesarrow_forwardTesting for a Vector SpaceIn Exercises 13-36, determine whether the set, together with the standard operations, is a vector space. If it is not, identify at least one of the ten vector space axioms that fails. The set of all 33 upper triangular matricesarrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning