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 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

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