EjrALGorto05

(%i2)

X :[ x, y, z, t] $
coef( expr) : = makelist( coeff( expr, X[ i]), i, 1, 4) $

Si $S=\{(x,y,z,t)\in\mathbb{R}^4;2x+3y-z=0,\, y+2z-t=0\}$. entonces

(%i5)

s1 : coef( 2 * x + 3 * y - z) $
s2 : coef( y + 2 * z - t) $
print( "S^⟂", "=Gen{", s1, ",", s2, "}") $

\begin{matrix} S^{⟂} =Gen {[2, 3, - 1, 0], [0, 1, 2, - 1]} \end{matrix}

El vector que pertenezca al ortogonal será aquel linealmente dependiente:

(%i10)

a :[ 8, 13, - 2, - 1] $
b :[ 8, - 13, 2, - 1] $
c :[ - 8, 13, - 2, 1] $
X :[ a, b, c] $
makelist( rank( matrix( X[ i], s1, s2)), i, 1, 3) ;

\begin{matrix} (%o10) & [2, 3, 3] \end{matrix}

Created with wxMaxima.