- #1

- 24

- 0

## Homework Statement

Consider the transformation T from ℝ2 to ℝ3 given by,

$$T\begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = x_1\begin{bmatrix} 1 \\ 2 \\ 3\end{bmatrix} + x_2\begin{bmatrix} 4 \\ 5 \\ 6\end{bmatrix}$$

Is this transformation linear? If so, find its matrix

## Homework Equations

A transformation is not linear unless:

a. T(v+w) = T(v) + T(w)

b. T(kv) = kT(v)

for all vectors v and w and scalars k in R^m

## The Attempt at a Solution

All I know right now are the two relevant equations that I posted, but I can't seem to find how to apply them here. I'm not sure how to work with all of these column vectors. Any help is appreciated

Last edited by a moderator: