1. ## question

how can prove that this array:

can be written as a linear combination in group :
؟.

2. Originally Posted by suliman
how can prove that this array:

can be written as a linear combination in group :
؟.
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.

3. thank you