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[SOLVED] whit.a.6.1 Show that the plane H defined by:

karush

Well-known member
Jan 31, 2012
2,836
$\tiny{whit.a.6.1}$

Show that the plane H defined by:

$H=\left\{
\alpha_1\left[
\begin{array}{rrr}1\\1\\1\end{array} \right]
+\alpha_2\left[\begin{array}{rrr}1\\-1\\0\end{array} \right]
\textit{ Such that } \alpha_1,\ \alpha_1\in\mathbb{R}\right\}
=\begin{bmatrix}a_1+a_2\\ a_1+a_2\\ a_1\end{bmatrix}$
$\text{rref}(H)=\left[ \begin{array}{cc|c} 1 & 0 & 0 \\ 0 & 1 & 0 \\0 & 0 & 0 \end{array} \right]$
ok I don't know what this answers
 
Last edited:

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
619
What question are you trying to answer?

The fact that
$H=\left\{
\alpha_1\left[
\begin{array}{rrr}1\\1\\1\end{array} \right]
+\alpha_2\left[\begin{array}{rrr}1\\-1\\0\end{array} \right]
\textit{ Such that } \alpha_1,\ \alpha_1\in\mathbb{R}\right\}$
IS the same as
$\begin{bmatrix}a_1+a_2\\ a_1+a_2\\ a_1\end{bmatrix}$
should be obvious from the definitions of "scalar multiplication" and "addition of vectors".

Or are you trying to say that something is true about that plane? If so, what?

($\left[ \begin{array}{cc|c} 1 & 0 & 0 \\ 0 & 1 & 0 \\0 & 0 & 0 \end{array} \right]$ doesn't appear to have anything to do with this problem and "$\text{rref}(H)$" doesn't make sense because "H" is plane, not a matrix.)
 

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
619
It's odd that Karush "liked" my response but did not answer the questions I asked.
 

karush

Well-known member
Jan 31, 2012
2,836
What question are you trying to answer?

The fact that
$H=\left\{
\alpha_1\left[
\begin{array}{rrr}1\\1\\1\end{array} \right]
+\alpha_2\left[\begin{array}{rrr}1\\-1\\0\end{array} \right]
\textit{ Such that } \alpha_1,\ \alpha_1\in\mathbb{R}\right\}$
IS the same as
$\begin{bmatrix}a_1+a_2\\ a_1+a_2\\ a_1\end{bmatrix}$
should be obvious from the definitions of "scalar multiplication" and "addition of vectors".

Or are you trying to say that something is true about that plane? If so, what?

($\left[ \begin{array}{cc|c} 1 & 0 & 0 \\ 0 & 1 & 0 \\0 & 0 & 0 \end{array} \right]$ doesn't appear to have anything to do with this problem and "$\text{rref}(H)$" doesn't make sense because "H" is plane, not a matrix.)
that was shown in an example