What would you like to understand?

The span of two nonzero, non-collinear vectors is the entire 2D plane. This means that by taking all possible linear combinations of these two vectors, you can reach any point in the plane.

Conditions: The two vectors are nonzero.; The two vectors are non-collinear (they do not lie on the same line).

The span of two nonzero, non-collinear vectors is the entire 2D plane. This means that by taking all possible linear combinations of these two vectors, you can reach any point in the plane.

Conditions: The two vectors are nonzero.; The two vectors are non-collinear (they do not lie on the same line).

A linear combination of two arbitrary non-collinear vectors $\vec{v}$ and $\vec{w}$ is formed by multiplying each vector by a scalar ($a$ and $b$) and adding them together ($a\vec{v} + b\vec{w}$). If both scalars are allowed to vary continuously across all real numbers, the tips of these combined vectors sweep out every possible point on the 2D plane.

Conditions: The two vectors $\vec{v}$ and $\vec{w}$ are non-collinear (point in different directions and do not lie on the same line).; The scalars $a$ and $b$ vary continuously across all real numbers.

A linear combination of two arbitrary non-collinear vectors $\vec{v}$ and $\vec{w}$ is formed by multiplying each vector by a scalar ($a$ and $b$) and adding them together ($a\vec{v} + b\vec{w}$). If both scalars are allowed to vary continuously across all real numbers, the tips of these combined vectors sweep out every possible point on the 2D plane.

Conditions: The two vectors $\vec{v}$ and $\vec{w}$ are non-collinear (point in different directions and do not lie on the same line).; The scalars $a$ and $b$ vary continuously across all real numbers.