Mathematics, 05.09.2020 20:01 jayzie1728
Express w as a linear combination of the vector V1 and V2 if this is possible. If not, Show that it is impossible.
w= [3]
[-1]
[2]
v1= [-3]
[1]
[2]
v2= [6]
[-2]
[3]
Answers: 1
![w=\left[\begin{array}{c}3&-1&2\end{array}\right]](/tpl/images/0743/5337/21796.png)
![V_{1}=\left[\begin{array}{c}-3&1&2\end{array}\right]](/tpl/images/0743/5337/f47bc.png)
![V_{2}=\left[\begin{array}{c}6&-2&3\end{array}\right]](/tpl/images/0743/5337/4d2f1.png)
as a linear combination of the vectors 
and 
, we will search for 
∈ IR such that : 
(I)![a\left[\begin{array}{c}-3&1&2\end{array}\right]+b\left[\begin{array}{c}6&-2&3\end{array}\right]=\left[\begin{array}{c}3&-1&2\end{array}\right]](/tpl/images/0743/5337/d17e9.png)
![\left[\begin{array}{ccc}-3&6&3\\1&-2&-1\\2&3&2\end{array}\right]](/tpl/images/0743/5337/e241e.png)
![\left[\begin{array}{ccc}1&0&\frac{1}{7}\\0&1&\frac{4}{7}\\0&0&0\end{array}\right]](/tpl/images/0743/5337/c116d.png)
and 
and 
in the equation (I) : 
⇒![(\frac{1}{7}).\left[\begin{array}{c}-3&1&2\end{array}\right]+(\frac{4}{7}).\left[\begin{array}{c}6&-2&3\end{array}\right]=\left[\begin{array}{c}3&-1&2\end{array}\right]](/tpl/images/0743/5337/dc677.png)
⇒![\left[\begin{array}{c}3&-1&2\end{array}\right]=\left[\begin{array}{c}3&-1&2\end{array}\right]](/tpl/images/0743/5337/ff1bf.png)
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Express w as a linear combination of the vector V1 and V2 if this is possible. If not, Show that it...
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