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## Homework Statement

Let y [itex]\in[/itex]ℝ[itex]^{3}[/itex] be a fixed vector, and define T:ℝ[itex]^{3}[/itex]→ℝ[itex]^{3}[/itex] to be Tx = X [itex]\times[/itex] Y, the cross product of x and y.

Show that T is linear.

## Homework Equations

## The Attempt at a Solution

For this question do we have to define another T with the cross product of two other variables to prove this?

For example:

Tx = x [itex]\times[/itex] y

Ta = a [itex]\times[/itex] b

and we can prove linearity by T(cx+da) = cTx + dTa ?

Solution in this problem is welcome, since this assignment is already overdue.

Thanks

## Homework Statement

## Homework Equations

## The Attempt at a Solution

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