- #1

karush

Gold Member

MHB

- 3,269

- 5

Determine if the set of vectors

$\begin{bmatrix}

x\\y\\3x+2y

\end{bmatrix}$ $\in \Bbb{R}^3$

form a vector space

(with the usual addition and scalar multiplication for vectors in $\Bbb{R}^3$).OK first of all this doesn't have z in it.

So I don't know if this meets the requirement of

whether number of elements in the set are equal to the dimension of given vector spaceOk I assume a matrix can be formed of this as albeit assuming

$x_1,x_2,x_3 \textit{ and } y_1,y_2,y_3$

$\begin{bmatrix}

1&0\\0&1\\3&2

\end{bmatrix}$

I don't see how this would be linearly independent

$\begin{bmatrix}

x\\y\\3x+2y

\end{bmatrix}$ $\in \Bbb{R}^3$

form a vector space

(with the usual addition and scalar multiplication for vectors in $\Bbb{R}^3$).OK first of all this doesn't have z in it.

So I don't know if this meets the requirement of

whether number of elements in the set are equal to the dimension of given vector spaceOk I assume a matrix can be formed of this as albeit assuming

$x_1,x_2,x_3 \textit{ and } y_1,y_2,y_3$

$\begin{bmatrix}

1&0\\0&1\\3&2

\end{bmatrix}$

I don't see how this would be linearly independent