Show-that-E-x-y-z-R-3-x-2y-z-0-is-a-subspace-vector-of-which-we-will-determine-one-base-please-help-sirs-

Question Number 79111 by mathocean1 last updated on 22/Jan/20

Show that

E = {(x, y, z) \in R^{3} / x - 2 y + z = 0}

is a subspace vector of which we

will determine one base .

please help sirs \dots

Commented by mathmax by abdo last updated on 22/Jan/20

x - 2 y + z = 0 \Rightarrow x = 2 y - z \Rightarrow (x, y, z) = (2 y - z, y, z)

= (2 y, y, o) + (- z, 0, z) = y (2, 1, 0) + z (- 1, 0, 1) = y \vec{u} + z \vec{v} \Rightarrow

E i s a v e c t o r i a l p l a n e w i t h b a s e B = (\vec{u}, \vec{v})

\vec{u} (2, 1, 0) a n d \vec{v} (- 1, 0, 1)

Commented by mathocean1 last updated on 22/Jan/20

thanks sir

Commented by mathmax by abdo last updated on 23/Jan/20

y o u a r e w e l c o m e