Let W be the subspace of R^4 generated by vector (1, − 2, 5, − 3), (2, 3, 1, − 4), (3, 8, − 3, − 5) find the basis and dimension of W.


Question and Answers Forum

All Questions Topic List
Vector Questions
Previous in All Question Next in All Question
Previous in Vector Next in Vector
Question Number 56899 by Tawa1 last updated on 26/Mar/19

$Let W be the subspace of R^{4} generated by vector$ $(1, - 2, 5, - 3), (2, 3, 1, - 4), (3, 8, - 3, - 5) find the$ $basis and dimension of W .$
	Answered by kaivan.ahmadi last updated on 26/Mar/19

	$\| \begin{matrix} 1 - 2 5 - 3 \\ 2 3 1 - 4 \\ 3 8 - 3 - 5 \end{matrix} \| \underset{- 3 R_{1} + R_{3}}{\overset{- 2 R_{1} + R_{2}}{\to}} \| \begin{matrix} 1 - 2 5 - 3 \\ 0 7 - 9 2 \\ 0 14 - 18 4 \end{matrix} \|$ $\overset{\frac{R_{2}}{7}}{\to} \| \begin{matrix} 1 - 2 5 - 3 \\ 0 1 \frac{- 9}{7} \frac{2}{7} \\ 0 14 - 18 4 \end{matrix} \| \underset{- 14 R_{2} + R_{3}}{\overset{2 R_{2} + R_{1}}{\to}}$ $\| \begin{matrix} 1 0 \frac{17}{7} \frac{- 17}{7} \\ 0 1 \frac{- 9}{7} \frac{2}{7} \\ 0 0 0 0 \end{matrix} \| \Rightarrow$ $d i m (W) = 2 = n u m b e r o f n o n z e r o r o w s$ $a n d t h e s e t o f n o n z e r o r o w s a s v e c t o r i s a b a s i s f o r W$
	Commented by Tawa1 last updated on 29/Mar/19

	$God bless you sir . I appreciate$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum