EjrALGsistema02

La variedad $\{(x,y,z,t,u)\in\mathbb{R}^5;x-2=y+3=z-1=t+2u\}$, cumple:

(%i2)

eq :[ x - 2 = y + 3, x - 2 = z - 1, x - 2 = t + 2 * u] $
makelist( print( eq[ i]), i, 1, 3) $

\begin{matrix} x - 2 = y + 3 \\ x - 2 = z - 1 \\ x - 2 = 2 u + t \end{matrix}

Resolvamos el sistema en $\mathbb{R}^5$

(%i3)

sol : linsolve( eq,[ x, y, z, t, u]) ;

\begin{matrix} (sol) & [x = %r2 + 2 %r1 + 2, y = %r2 + 2 %r1 - 3, z = %r2 + 2 %r1 + 1, t = %r2, u = %r1] \end{matrix}

(%i7)

P : ev([ x, y, z, t, u], ev( sol, %rnum_list[ 1] = 0, %rnum_list[ 2] = 0)) $
v1 : ev([ x, y, z, t, u], ev( sol, %rnum_list[ 1] = 1, %rnum_list[ 2] = 0)) - P $
v2 : ev([ x, y, z, t, u], ev( sol, %rnum_list[ 1] = 0, %rnum_list[ 2] = 1)) - P $
print( transpose( matrix([ x, y, z, t, u])), "=", transpose( matrix( P)), "+ λ",
transpose( matrix( v1)), "+ μ",
transpose( matrix( v2))) $ ;

\begin{matrix} [\begin{matrix} x \\ y \\ z \\ t \\ u \end{matrix}] = [\begin{matrix} 2 \\ - 3 \\ 1 \\ 0 \\ 0 \end{matrix}] + λ [\begin{matrix} 2 \\ 2 \\ 2 \\ 0 \\ 1 \end{matrix}] + μ [\begin{matrix} 1 \\ 1 \\ 1 \\ 1 \\ 0 \end{matrix}] \end{matrix}

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