System of equations

**Ideasman** · November 13th 2007, 09:55 PM

I have to solve these systems in succession, and I don't know how:

$\left[ \begin {array}{ccc} 0&0&0\\\noalign{\medskip}-1&1&-1\\\noalign{\medskip}0&1&-1\end {array} \right]P = \left[ \begin {array}{c} 0\\\noalign{\medskip}1\\\noalign{\medskip}1<br /> \end {array} \right]$

$\left[ \begin {array}{ccc} 0&0&0\\\noalign{\medskip}-1&1&-1\\\noalign{\medskip}0&1&-1\end {array} \right]Q = P$

I need P and Q

**Peritus** · November 14th 2007, 01:57 AM

P = transpose[(p1,p2,p3)]
Q = transpose[(q1,q2,q3)]

-p1+p2-p3 = 1
p2 - p3 = 1
-----------------
p1 = 0, p2 = 1+p3

~~~~~~~~~~~~~~~~~
-q1+q2-q3 = p2
q2 - q3 = p3
----------------
-q1 = p2-p3 = 1 --------> q1= -1
q2 = p3 + q3

P = transpose[(0, 1+p3, p3)]

Q = transpose[(-1, p3 + q3, q3)]

which means you've got 2 D.O.F's let's choose for instance q3 = p3 = 0

P = transpose[(0,1,0)] Q = transpose[(-1,0,0)]

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