Consider the subspace H of R* given by H = 2a 2a8b2c -4a+20b5c 2a + 166 - 4c a. Find a basis for H. (Note: Use one vector per answerbox. It's okay if some of the answerboxes remain empty.) { } Why am I not getting partial credit? b. State the dimension of H. dim (H) = = : a, b, c ER RACER}

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
icon
Related questions
Question

I need help with this problem

Consider the subspace \( H \) of \( \mathbb{R}^4 \) given by

\[
H = \left\{ \begin{bmatrix} 2a \\ 2a + 8b - 2c \\ -4a + 20b - 5c \\ 2a + 16b - 4c \end{bmatrix} : a, b, c \in \mathbb{R} \right\}.
\]

a. Find a basis for \( H \).  
(Note: Use one vector per answerbox. It's okay if some of the answer boxes remain empty.)  
\[ \{ \, \,\, \, , \, \,\, \, , \, \,\, \, \, \} \]  

Why am I not getting partial credit?

b. State the dimension of \( H \).  
\[ \text{dim}(H) = \, \,\, \, \]
Transcribed Image Text:Consider the subspace \( H \) of \( \mathbb{R}^4 \) given by \[ H = \left\{ \begin{bmatrix} 2a \\ 2a + 8b - 2c \\ -4a + 20b - 5c \\ 2a + 16b - 4c \end{bmatrix} : a, b, c \in \mathbb{R} \right\}. \] a. Find a basis for \( H \). (Note: Use one vector per answerbox. It's okay if some of the answer boxes remain empty.) \[ \{ \, \,\, \, , \, \,\, \, , \, \,\, \, \, \} \] Why am I not getting partial credit? b. State the dimension of \( H \). \[ \text{dim}(H) = \, \,\, \, \]
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education