how can prove that this array:

can be written as a linear combination in group :

؟.

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- Aug 29th 2009, 06:47 PM #1

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- Aug 29th 2009, 07:06 PM #2

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It is the same with verifying the linear dependence of the vectors. you can just regard the 2*2 matrix as 4*1 vector.

So the problem is to check whether the equation groups

$\displaystyle \alpha_{1}+\alpha_{2}+4\alpha_{3}-2\alpha_{2}=3$

$\displaystyle 2\alpha_{1}+2\alpha_{2}+\alpha_{3}+3\alpha_{2}=6$

$\displaystyle 6\alpha_{1}+\alpha_{2}-2\alpha_{3}-\alpha_{2}=-2$

$\displaystyle -5\alpha_{1}+3\alpha_{3}+2\alpha_{2}=5$

is solvable.

- Aug 29th 2009, 11:38 PM #3