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Find the base and dimension of a linear space
: 18 gru 2021, 01:46
autor: Boyce
Find the base and dimension of a linear space \(V⊂ℝ^3\) spanned on vectors:
\(( 2 , - 1 , 1 ) , ( - 2 , 2 , 1 ) , ( 0 , 1 , 2 ) , ( - 2 , 3 , 3 ) , ( 1 , 0 , 1 )\)
Re: Find the base and dimension of a linear space
: 18 gru 2021, 11:36
autor: panb
Boyce pisze: ↑18 gru 2021, 01:46
Find the base and dimension of a linear space
\(V⊂ℝ^3\) spanned on vectors:
\(( 2 , - 1 , 1 ) , ( - 2 , 2 , 1 ) , ( 0 , 1 , 2 ) , ( - 2 , 3 , 3 ) , ( 1 , 0 , 1 )\)
You need to find the rank of this matrix (using any method you've learned)
\[ \begin{bmatrix}2&-1&1\\-2&2&1\\ 0&1&2\\-2&3&3\\1&0&1 \end{bmatrix} \]
Hint:
\( \begin{vmatrix}0&1&2\\-2&3&3\\1&0&1 \end{vmatrix} =2\neq0 \)