Hello, Please need your help Let B ={(1,2, 3), (3, 2, 1), (0,0, 1)}. Show that B is linearly independent and spansR³. Show all of your work for credit.

Answered: Let B {(1,2,3), (3, 2, 1), (0,0, 1)}.…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

Hello, Please need your help

Let B =
{(1,2, 3), (3, 2, 1), (0,0, 1)}. Show that B is linearly independent and spans
R³. Show all of your work for credit.

Expert Solution

Step 1

In this question, concept of linear span is used.

Linear span
Let $V$ represent a vector space, and $S = (v_{1}, v_{2}, . . . . . ., v_{n})$ represent a subset of V. If every vector $v$ in $V$ can be expressed as a linear combination of vectors in S, we say S spans $V$ .
The smallest linear subspace that contains a set S of vectors (from a vector space), written span(S), is termed the linear span (sometimes called the linear hull or just span) in mathematics. It can be defined as the intersection of all linear sub-spaces containing S, or as a set of linear combinations of elements of S. A vector space is defined as the linear span of a set of vectors. Matroids and modules can be generalised to spans.