Linear Algebra and Its Applications, 5th Edition
Authors: David C. Lay, Steven R. Lay, Judi J. McDonald
ISBN-13: 978-0321982384
We have solutions for your book!
See our solution for Question 20E from Chapter 1.3 from Lay's Linear Algebra and Its Applications, 5th Edition.
Problem 20E
Chapter:
Problem:
Give a geometric description of Span {v1, v2} for the vectors
Step-by-Step Solution
Given Information
We are given with following vectors: \[ \mathbf { v } _ { 1 } = \left[ \begin{array} { l } { 3 } \\ { 0 } \\ { 2 } \end{array} \right] , \mathbf { v } _ { 2 } = \left[ \begin{array} { c } { - 2 } \\ { 0 } \\ { 3 } \end{array} \right] \] We have to give geometric description of Span{$v_1$, $v_2$} for the vectors $v_1$ and $v_2$.
Step-1:
If $u$ and $v$ are nonzero vectors in $R^3$, which are linearly independent, then their Span is a plane in $R^3$ containing vectors {\bf{u}}, {\bf{v}} and {\bf{0}}
Therefore,
Span{$v_1,v_2$} os a plane in $R^3$ passing through the origin
We are given with following vectors: \[ \mathbf { v } _ { 1 } = \left[ \begin{array} { l } { 3 } \\ { 0 } \\ { 2 } \end{array} \right] , \mathbf { v } _ { 2 } = \left[ \begin{array} { c } { - 2 } \\ { 0 } \\ { 3 } \end{array} \right] \] We have to give geometric description of Span{$v_1$, $v_2$} for the vectors $v_1$ and $v_2$.
Step-1:
If $u$ and $v$ are nonzero vectors in $R^3$, which are linearly independent, then their Span is a plane in $R^3$ containing vectors {\bf{u}}, {\bf{v}} and {\bf{0}}
Therefore,
Span{$v_1,v_2$} os a plane in $R^3$ passing through the origin