Consider the vectors $x_1=(2,1),x_2=(4,3),x_3=(7,-3)$:
(a) Show that $x_1$ and $x$ form a basis for $\mathbb{R}^2$.
(b) Why must $x_1,x_2,x_3$ be linearly dependent?
(c) What is the dimension of $\textrm{Span}(x_1,x_2,x_3)$?
Especially for question (c), I just don't understand how to find the dimension of a Span.]1
$x_1$ and $x_2$ are linearly independent. The dimenson of $\mathbb R^2$ is 2. Any two linearly independent vectors from $\mathbb R^2$ spans $\mathbb R^2$
Since $x_3$ is a vector in $\mathbb R^2$ and $\{x_1,x_2\}$ span $\mathbb R^2$ then $x_3$ is in Span $(x_1,x_2)$
or, more directly $x_3 = 12x_1 - 17 x_2$
Again, any two of the 3 vectors spans $\mathbb R^2$ the third is redundant. Nonethless Span $(x_1,x_2,x_3)$ is $\mathbb R^2$