Linear Algebra and Its Applications, 5th Edition
Authors: David C. Lay, Steven R. Lay, Judi J. McDonald
ISBN-13: 978-0321982384
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See our solution for Question 10E from Chapter 4.1 from Lay's Linear Algebra and Its Applications, 5th Edition.
Problem 10E
Chapter:
Problem:
Let H be the set of all vectors of the form Show that H is a subspace of ℝ3. (Use the method of Exercise .) Let H be the set of all vectors of the
Step-by-Step Solution
Given Information
We are given with set of vectors of the form \[H = \left[ {\begin{array}{*{20}{c}}{2t}\\0\\{ - t}\end{array}} \right]\]We have to show that H is a subspace of $R^3$
Step 1: The parametric form
Write the vector in parametric form\[H = \left[ {\begin{array}{*{20}{c}}{2t}\\0\\{ - t}\end{array}} \right] = t\left[ {\begin{array}{*{20}{c}}2\\0\\{ - 1}\end{array}} \right]\]
Step 2: Subspace of H
By definition of Span of a vector, we can see that the vector Span{V} is a subspace of H. So, H is subspace of $R^3$
We are given with set of vectors of the form \[H = \left[ {\begin{array}{*{20}{c}}{2t}\\0\\{ - t}\end{array}} \right]\]We have to show that H is a subspace of $R^3$
Step 1: The parametric form
Write the vector in parametric form\[H = \left[ {\begin{array}{*{20}{c}}{2t}\\0\\{ - t}\end{array}} \right] = t\left[ {\begin{array}{*{20}{c}}2\\0\\{ - 1}\end{array}} \right]\]
Step 2: Subspace of H
By definition of Span of a vector, we can see that the vector Span{V} is a subspace of H. So, H is subspace of $R^3$