[LA] help understading a best solution problem

Question

ganeshie8 · Answer

find the best possible values for $x_1 $ and $x_2$ :

$$ \large    

\left[ \begin{array}{cc}

1&1 \
1&2 \
1&3 \
\end{array} 

\right]

\left[ \begin{array}{c}

x_1 \
x_2 \
\end{array} 

\right]

=
\left[ \begin{array}{c}

1 \
2 \
3 \
\end{array} 

\right]

$$

mathmate · Answer

(0,1) would do, wouldn't it?

ganeshie8 · Answer

Oh yes sorr made a typo... let me fix it :)

$$ 

\left[ \begin{array}{cc}

1&1 \
1&2 \
1&3 \
\end{array} 

\right]

\left[ \begin{array}{c}

x_1 \
x_2 \
\end{array} 

\right]

=
\left[ \begin{array}{c}

1 \
2 \
\color{red}{2} \
\end{array} 

\right]

$$

anonymous · Answer

x1+x2                       1
x1+2x2             =      2
x1+3x2                      2

ganeshie8 · Answer

exactly! those are the system of equations we want to solve

ganeshie8 · Answer

this problem is equivalent to finding the best fit line for points :  
$\large  {(1,1), (2,2), (3,2)}$

i am familiar with the calculus method of finding the best fit line, but the matrix method is just throwing me off as im not that good with substpaces and related stuff... :(

anonymous · Answer

http://books.google.co.in/books?id=CbIqX6TxJVMC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false

anonymous · Answer

books.google.co.in/books/about/Engineering_Mathematics_Vol_1.html?...

anonymous · Answer

books.google.co.in/books?isbn=8190693549

anonymous · Answer

mathforcollege.com/nm/mws/gen/04sle/mws_gen_sle_bck_system.pdf

anonymous · Answer

www.math.tamu.edu/~shatalov/Tan_chpt2.pdf

anonymous · Answer

www3.ul.ie/~mlc/support/Loughborough%20website/chap8/8_2.pdf

anonymous · Answer

www.math.ku.edu/~lerner/LAnotes/LAnotes.pdf

anonymous · Answer

https://docs.google.com/viewer?url=http://cims.nyu.edu/~kiryl/teaching/la/les082903web.pdf

anonymous · Answer

first two eqn solving we get x1x2 (-2,-1)

anonymous · Answer

2nd and 3rd eqn we get x1x2 (2,0)

anonymous · Answer

solving 1st and 3rd we get x1x2 (1/2,1/2)

ganeshie8 · Answer

yes we don't get a straight line :

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