- #1

VinnyCee

- 489

- 0

## Homework Statement

For two nonparallel vectors [itex]\overrightarrow{v}[/itex] and [itex]\overrightarrow{w}[/itex] in [itex]\mathbb{R}^3[/itex], consider the linear transformation

[tex]T\left(\overrightarrow{x}\right)\,=\,det\left[\overrightarrow{x}\,\,\overrightarrow{v}\,\,\overrightarrow{w}\right][/tex]

from [itex]\mathbb{R}^3[/itex] to [itex]\mathbb{R}[/itex]. Describe the kernel of T geometrically. What is the image of T?

## Homework Equations

I have no idea. Maybe the equations on how to find a kernel and image?

## The Attempt at a Solution

I don't know where to even start this exercise! How does one "describe geometrically"?